Was hoping a post-op guy would answer this. It's an interesting question. Hope you don't mind a speculative answer.
The type of phalloplasty (and erectile device, if present) could affect this. A semi-malleable rod, for example, probably prevents buoyancy. Inflatable erectile device, probably not. Forearm or ALT phalloplasty, mostly skin and subcutaneous fatty tissue, probably floats to some degree. Phalloplasty variations which use some amount of muscle tissue in the construction probably wouldn't float as easily.
According to my DuckDuckGo results (I will not have Google knowing I searched for this, nnnnnope) it's normal for a penis to float in water. So if you were concerned and not just curious: A) non-surgically constructed penises float too B) for this very reason, there's bound to be men's swimwear designed to prevent aquatic awkwardness.