> You have a high pressure helium tank, closed, but connected to a large empty balloon, underwater. You open the tank and fill the balloon with a significant volume (should work if enough pressure in the tank). Will the system start floating?

If the balloon is big enough, yes.

Exactly the same thing will happen as if you do it in normal air. Imagine hooking up a very high pressure helium tank to a blimp, and inflating the blimp, so that it takes off with the tank attached.