Why not? I doubt there are any legal restrictions other than don't be a hazard to navigation. But it would probably be too small to be a hazard anyway, and likely too small to be noticed.

Yes you can. However, international waters are a physically challenging environment and getting there requires navigating national waters which have regulatory restrictions. Of course, enforcement is probably nonexistant if you're small, barely visible, and heading straight out to sea... so, solve the "invisible awesome robot that can survive in tough conditions" problem, stock the "multi-day batteries for energy continuity" load, buy the "expensive communications" solution, and then yeah - you too can play with the big boys in the bathtub. Or ... just stick to your actual bathtub.