Weird & Interesting science, take 2

[classicdrogn]

I was reading about the tragic fate of poor U.S.S. Grunion and wandered off into a crush-depth related tangent, which can beb summarized into the outline of a practical physics experiment. Most of the time a pressure vessel encounters crush depth it breaks up and releases anything bouyant to float away while the rest sinks, but what if the system as a whole remained intact enough for only not to be part of the picture?

First, assume sea access, or a sufficiently large container of water. The experiment device itself is a test tube or similar vessel of gas at waterline pressure capped with a piston that keeps it from escaping but allows water pressure to compress it as it is submerged. The tube assembly is weighted to bet just buoyant enough to float when placed on the surface of the water. Assume that you wait between each depth change to allow temperature to normalize so only the change in gas pressure is a factor. Since compressed gas is denser than sparse gas at the same temperature, is there a point at which the water pressure will compress the gas enough that the assembly no longer has positive buoyancy? By logic it should, but my logic is not always like your Earth-logic, and what the actual laws of physics have to say about things can be counterintuitive at times.