Not directly, no. But if you stole one, you likely wouldn't get very far before the US military or Coast Guard caught up with you, making guarding it directly largely unnecessary.
Let's talk about the big picture first. I'm assuming that their navy doesn't openly sail up and grab our stuff in the Atlantic (which has happened elsewhere, but in their backyard, not the United States'). That wouldn't end well at all being right off the US coast. As such, I assume President Weisenheimer want to do this with some plausible deniability if it goes badly.
Logistics are a problem
Assuming you want to steal the rocket, you need to
- Get close to the rocket
- Steal the rocket (or the whole drone ship)
- Get it somewhere to learn what you want to about it (or refuel and use it yourself)
Let's ignore the other issues for a moment. A submarine isn't how you would do it. The rocket isn't going to fare well underwater. It's not designed for that kind of thing. The electronics alone won't last, let alone things like the fuel tanks. SpaceX might have recovered the one that soft landed in the ocean, but that one was left floating and it wasn't in the water for a long time. Unless the offending country here was somewhere close to the US, you're going to have to tow this thing for days or weeks in the ocean. Even if you didn't care and dragged it underwater anyways, you probably won't get very far with it. Your speedy sub is now dragging a rocket behind. Even if you encased it in something, you've got to work much harder to pull it now.
Then you have the problem that you can't move very fast. Even if you put a dive team on the drone ship and steal it too, it doesn't move very fast (it's basically a barge after all). Towing it, or stealing the barge, isn't going to get you very far.
The next best solution would be that you've sailed your larger cargo container ship (that really isn't a cargo ship) up to it and you grab it with a crane, and haul it in. Again, you're not moving very fast and, most importantly, you would be noticed
Global Fishing Watch, a tool launched publicly on September 15, maps out broadcast data that tracks ships using satellites. The tool can track the path of ships over time, and identify suspicious patterns that indicate either overfishing or illegal fishing.
Tracking boats by satellite is so easy a
caveman fishing activist group can do it. You think SpaceX or the US government would notice your large boat in the area when the booster disappeared?
The military isn't that far off
SpaceX operates out of Vandenberg Air Force Base on the west coat, and Cape Canaveral Air Force Base on the east coast. There are major US Navy bases all up and down the California and Florida coastlines. Additionally, there's the Coast Guard (although they can only operate in US water). To say that there would be a fast response would be an understatement. All SpaceX would have to do is tell the Air Force that their booster was snatched and people would start looking.
Once you found your culprit, they would probably send a US Navy cruiser out (or a Coast Guard Cutter if it were closer to shore). Remember how I emphasized how slow the thieves were going? Cruisers and Cutters are not slow and they will catch up.