While think an air propelled bot is never going to win a match, it would be interesting to see. Here are some ideas:

Rather than use propellers, use ducted fans meant for jet aircraft models; they produce more thrust in a smaller diameter package. Some of the Hobbyking ones come with matched motors. The enclosed fan blades will be safer and probably less breakable.

Steering the bot is going to be interesting; you won't really have a reverse as such although you could mount the fans at both ends to give you thrust in both directions. Steering left & right has several options: using moving vanes like hovercraft use is probably too delicate to survive a full combat match. You could possibly mount the fans on swivels and move them to steer like a jet ski does. If you use two fans at each end, you could try proportional mixing to turn the bot. This is the simplest from a mechanical standpoint but might not produce sharp turns. Finally, you can use wheels with Ackerman steering but again, that may be too delicate to survive long.

My favourite steering idea is to use three fans in a 120 degree radial pattern and control them with an OMX-3 omni directional mixer. It may or may not work but an omni directional air powered bot would be really unique!

If you go for air-powered steering, use ball transfer rollers rather than wheels. They are compact and tough, plus you can mount them on the top & bottom of the bot for full invertability.