Condensation shouldn't be an issue as long as you're not cooling below the current dew point.
However, after experiencing one of these underfloor cooling systems once, I can say that the biggest issue is that cold air tends to be heavier and thus stay down. So in order to cool the entire room, not just the layer of air right above the floor, you need something to move the air, which is probably why they're providing fans. Either that or you can just lie on the floor all the time...
Floor heating works because warm air rises. I never understood why 'floor' cooling wasn't piped through the ceiling, instead. There are probably some engineering or heat transfer issues there, though.