When a spacecraft performs a splashdown maneuver, a recovery team is standing by to retrieve the capsule and its human contents quickly. A flotation collar is deployed to increase buoyancy and prevent the spacecraft from sinking. If, however, the spacecraft did sink, would it be able to withstand the pressure of the deep?
Structurally speaking, what are the differences between a spaceship floating in the vacuum of space and a submarine floating underwater in an ocean?
Let's differentiate "spacecraft" and "landing capsule".
There are various phases of the flight with various prerequisites, and several different (considerably different) designs of spacecrafts.
First, let's take the capsule. It must withstand violent reentry, unequal air pressures - the exposed side heats up enormously due to air friction, which is connected with quite huge pressure. It doesn't need to be lean and aerodynamic, quite opposite, it's one big airbrake with a passenger cabin attached to the trailing side. The pressure is largely unidirectional and primarily overheated, so the construction concerns of submarine are really distantly related, with its omnidirectional pressure, ability to withstand unexpected pressure waves (explosions), lean shape to minimize resistance, and ubiquitous water cooling making overheating non-issue.
Next, the orbital craft. To get there it must be be light. A mild kick could have pierced Apollo lunar module walls, ISS is more sturdy but still it's to withstand 1 bar pressure difference towards the outside (that's equivalent of mere 10m submersion depth), and again - towards the outside, that means no need for cross-beams to prevent buckling; it has natural tendency to bloat like a balloon. It isn't lean or aerodynamic in the least, air resistance is not a concern. Its construction problems are much closer to these of airplane hull than to that of a submarine.
And finally, the launch vehicle. This one does have to be lean, but again, it needs to be light. It is not resistant to lateral forces (its own acoustic wave reflected from the tower could damage it!), and again it doesn't have to withstand high outer pressures. The shuttle main fuel tank depends on internal fuel pressure; in other cases the structure is mostly unpressurized shell that allows air pressure to escape as it leaves the atmosphere, providing structural integrity but not isolating the inside - except for the relatively tiny human compartment.
Really, submarines with a considerable fraction of a meter thick solid metal shell, and designed for battle conditions - stealth, maneuverability, durability, weapons, aquatic environment - face entirely different construction challenges. On the other hand, there's much more overlap with airplanes.
Spacecraft are designed to contain internal pressure of not more than one atmosphere; submarines are designed to withstand dozens of atmospheres of external pressure. Furthermore, aerospace systems have very severe weight budgets - additional weight means additional fuel to power the engines to lift it, which itself adds weight... too much and the system will be unable to achieve its mission objective, or perhaps even get off the ground. Submersibles also have weight budgets, but they are nowhere as severe. The structural members of a spacecraft hull are predominantly operating in tension, at a significant fraction of the material's yield limits, and the most likely failure mode would be tensile fracture. The structural members of a submarine hull are predominantly operating in compression, and the most likely failure mode would be buckling.
Obviously, the space and undersea environments are entirely different and present entirely different challenges to vehicle designers and structural engineers. So, no, the requirements are not at all similar.
Given all of the above, one could reasonably deduce that if one were to (hypothetically) seal up and submerge a space capsule, its structure would buckle (it would be crushed) at relatively shallow depth. Capsules such as Mercury, Gemini, and Apollo had sufficient bouyancy to float on the ocean surface. As long as the hatches and vents remained closed to prevent ingres of water, they could remain afloat indefinitely. They could only be submerged if there was opportunity for water to enter (and displaced air to escape). In such case there would be no pressure differential on the hull to crush it no matter how deep it sunk.
As to the flotation collars, they were needed to stabilize the capsule (keep them upright in the water) and ensure bouyancy after the hatch was opened.
As far as I am aware, only one landing vehicle was not reclaimed before it sank to the bottom of the see (Liberty Bell 7). It was recovered in 1999 after spending 38 years on the bottom of the sea. The Liberty Bell 7 sunk after the hatch blew away prematurely and the capsule filled with water. Due to the fact there was both water on the inside and the outside of the capsule, the recovery report will not give much information about deep sea pressure on the whole capsule. It will however give an insight about the effect of sea water on the hull, and the effect of sea water and pressure on various instruments.
An inspection of the Mercury capsule, Liberty Bell 7, and its contents was made on September 1 and 2, 1999. The condition of the capsule and its contents was consistent with long-term exposure to salt water and high pressures at the bottom of the ocean. Many of the metallic materials suffered corrosion, whereas the polymer-based materials seem to have survived remarkably well. No identifiable items or structures were found that appeared to have any scientific value. At this time, no further nondestructive evaluation appears to be justified.
Abstract "Liberty Bell 7 Recovery Evaluation and Nondestructive Testing" [1]
This is worked out better in the article:
The external structure was in surprisingly good condition. (See fig. 3.) The black object at the bottom of the capsule is a skirt that provided ballast support. The heat shield would have been below the skirt, but the heat shield was missing and had not been recovered. The bottom structures included the flexible skirt and various metal strips and springs, a covering that appeared to be a polymer-based material, and the capsule base behind that; all looked to be in good condition. The external covering of the cone-shaped sides of the capsule consisted of small sheet-metal corrugated panels approximately 0.031 inch thick, which showed no signs of corrosion.
And later
The upper portion of the capsule, which was made of thick aluminum plates, experienced significant material loss caused by corrosion. Although some areas measured full thickness of approximately 0.220 inch, most regions were less, including several areas where the material was completely lost. Attached to these aluminum plates were large nodules of corrosion products.
However, when sea water meets the interior of the landing capsule, it will destroy almost anything, either by pressure or corroding.
As a last note: The report mentions exact the exact thickness of various parts of the hull. While the heat shield will shield the 0.031 inch (0.7874 mm) thick metal sheet at the bottom from heat, I doubt the heat shield will shield it from the sea pressure. Eventually the heat shield will completely corrode away too. While I have no exact numbers, I doubt the (thick?) 0.220 inch (5.58 mm) aluminium sheets will protect against even the slightest sea pressure either if the hull was completely waterproof. I have however no exact numbers to proof this.
While landing capsules have been improved a lot since then, I doubt there have been much improvements in "the survivability of a landing capsule on the bottom of the ocean".
[1] Liberty Bell 7 Recovery Evaluation and Nondestructive Testing, E. Madaras & W. Smith, December 1999. Accessed August 31, 2013.
