Consider for a moment a $100 air compressor with an impact driver on the end of the hose.
Imagine you've worked out some kind of adaptor that this impact driver can hold onto on one of your bike's wheel hubs. Now you hit the trigger and the impact driver is spinning your wheel.
A fairly cheap impact driver is capable of delivering maybe 125 ft/lbs of torque. Really I'm guessing there. It's been a long time since I've actually taken a look at the matter. But let's imagine I've got it right. The real world values are bound to be close.
Since the tire surface on a 26 inch wheel is fairly close to one foot from the axle, we can round things off and figure that the 'driving force' being applied to the road is 125 lbs. This is respectable, but it's not huge. If you relied on this much torque to get going from a complete stop, it would be a slow speed-up. But I imagine it would be plenty of torque while you're rolling, particularly if you helped with pedaling.
Of course you'll have to carry an air tank on your bike. And I suspect that one of those $20 air tanks might not give you much range. I could picture a small tank built to nuclear bomb specs that would allow you to compress a whole lot more air than a cheap tank would. But you'd need a better air compressor than the one we've imagined above. The tank itself would be fairly heavy. And if you were really cramming a lot of air into it, then the weight of the air itself might start adding up.
I don't know how close I am to the real truth in this matter. But I suspect that a pneumatic drive train might well be do-able in theory, but very cumbersome in practice.
Sorry. I don't want to be discouraging.
And if you prove me wrong, that'd be pretty cool.