Speaking as an actual engineer, no. It's not possible with modern technology, let alone the century old technology of the game. If you actually take a look at the balloons which are holding these buildings up, they are far too tiny to lift such a weight, even if they were filled with hydrogen instead of helium. A big enough balloon could lift it, but:
1) it would have to go above the buildings, not below, to maintain stability, which would block out all that lovely sunlight.
2) the buildings would not look like that - their structure would have to be completely different to account for being supported from above instead of by foundations from below. Doing that to a normal pre-depression era building would make it fall to pieces.
Also, hydrogen and helium would leak out of the balloons, so there's no way the city could survive like that for very long without replenishing its lifting gases.
So yeah, it's not realistic. But it's still a pretty awesome setting for a game.