No. Absolutely not.
1) Submarines are prohibitively heavy. Like... WAYYYY too heavy. You couldn't get one into space.
2) If you could do it piece-meal, it would take many, many launches to get all the pieces of the submarine into space, which would blow your budget.
3) One of the biggest problems in space that has mostly gone unrecognized by the general public is that of radiation. On Earth (underwater or not), we have the benefit of Earth's magnetic field that protects us from the worst of the Sun's radiation, as well as cosmic radiation. Spacecraft have little such benefit, and a submarine isn't designed to provide any further radiation protection than existing spacecraft.
4) Nuclear power in space is problematic from a political/bureaucratic perspective. Governments are reluctant to allow the construction of even the simplest of nuclear power sources due to launch risks. If the launch rocket blows up, where does the fallout land? Who collects it? Imagine a situation where a rocket containing nuclear fuel blows up, and that nuclear material then falls back to Earth into the hands of a terrorist organization. Not pretty.
If humans are going to put an actual spaceship into space, they will have to build it in space. It won't be something we have here on Earth that is re-purposed for use in space. And it will cost much more than 500M dollars. The cost of launching the construction materials into space cost about 100M dollars per launch. That doesn't count the cost of the materials themselves, the cost of developing a way to build it, or paying people to actually build the thing.