After a recent request, I got to thinking about the issue of buoyancy in air, and I think I may have changed my mind slightly about it. This is how it goes:
An inflated adult could only become buoyant if they were inflated with a very large volume of a lighter than air gas, probably either hydrogen or helium. Assuming they weigh 60 kg, they would have to become a sphere more than fifteen feet across for this to work, even assuming they are filled with a gas of zero density. It would be compressed anyway, meaning it would be denser.