No, operating a "stateless" vessel is what will get you arrested. So long as they flag this thing, they'll be fine.

I also doubt that they will scuttle the sub if intercepted by the navy.

The point is that the buoyancy allowed it to float up a bit, causing water to flow over the propulsion surfaces. That flow, however slight, moved the sub forward. That's actually rather impressive, considering most subs sink like a freaking rock or bob like a log (depending on their buoyancy) instead of moving forward while bobbing slightly. The speed of said forward motion wasn't stated that I saw but it speaks to the fact that it ought to work. Now to see if ti works as well as they think it will.

From the article, he's going to dive to 20 meters for about 45 minutes periodically (full article link: http://www.newscientist.com/article/mg20126936.900-across-the-ocean-in-a-pedalpowered-submarine.html?full=true [newscientist.com] scrollbar about 1/2 way).

Hope they have better luck than the human-powered Hunley, a Confederate sub that sank a US ship then itself sank on the way back in. First sub to sink a warship!

http://en.wikipedia.org/wiki/H.L._Hunley

Does Saudi Arabia get to arrest people who don't pray to Mecca five times a day while in international waters?

If they are on validly foreign-flagged ships, they are prohibited from doing so under international law (e.g., the Convention on the High Seas, 1958).

Stateless vessels are not protected in the same way.

In their own territory, sure but since the US didn't ratify the UN Conventions on the Law of the Sea they (should) still abide by the olden laws of the high seas which allowed for everybody to do whatever they want except for 'enemies of mankind' which are mainly pirates and slave traders.

The US considers almost the entirety of UNCLOS to be binding as declarative of customary international law; its objection to ratification centers pretty much entirely on the parts related to undersea mining in international waters.

Even under the new conventions they would have to abide by the laws of or deliver them to the country which flag the vessel flies under.

The US laws at issue apply to stateless vessels, who either don't fly a flag or who lose the protection of any flags flown by flying multiple flags of convenience (see Convention on the High Seas, 1958, Art. 6, Sec. 2.)

Wipedia says:
"A submarine is a watercraft capable of independent operation below water. It differs from a submersible, which has only limited underwater capability." I don't believe depth comes into play, either.

From the story, there's a link that says "2 more pictures". http://www.newscientist.com/articleimages/mg20126936.900/1-across-the-ocean-in-a-pedalpowered-submarine.html [newscientist.com] (total of 3). Picture 1 can be seen in the article. Picture 2 is a drawing. Picture 3 is a blue-line.

I doesn't squish the person inside, the person inside is basically a SCUBA diver. The effects of depth on SCUBA divers is well known.

I'm not sure how long you can stay down at 2 meters without decompressing, it's not on the dive tables since most divers dive further. I would guess you could stay a 2 meters all day without having to decompress on the way up.

All day at more than 5 or 10 meters, or for any time at more than 10 meters, you'd have to start paying attention to decompression.

At more than 30 meters, things start to get complicated.