In theory, there's no reason it couldn't have worked at all. The engine part of a steam engine wouldn't really know or care that whether the high pressure gas you ran though it was steam or pressurized air. They just used steam, because it's pretty easy to store water, and boil it to get steam as a source of the pressurized gas to run the engine.
Nonetheless, let's try to keep things in perspective. For comparison, a steam locomotive typically used about 100-200 gallons of water per mile. Water expands by about 1600:1 when it's boiled. So for a steam locomotive, you need something like 1600x150 = 240,000 gallons of compressed steam per mile.
Depending on the pressure you used, you'd need about the same amount of compressed air. Let's say our aircraft needs 500 feet to take off, and we design it to run out of compressed air just as it takes off. Further, let's say it needs 1% of the power of a locomotive. That means we still need: 240,000 * 0.01 * 500/5280 = ~225 gallons of compressed air.
But that's not really powered flight, just powered take-off roll, followed by an unpowered glide and a landing.
I'm not at all sure we can extend that ever having even a hope of, say, 1 mile of powered flight. For 1 mile (plus takeoff roll), we need a pressure tank close to 3000 gallons, which (even with modern technology) weighs close to 4000 pounds. With a 4000 pound tank, our aircraft would probably need to weigh at least 4500 pounds. And to power that, we'd need a bigger engine that used more compressed air--and we're almost immediately caught in a vicious circle of bigger tank -> bigger aircraft -> bigger engine -> still bigger tank.
You can undoubtedly come up with a better estimate that this though. In particular, I've pretty much just pull the "1%" number out of the air. You can obviously come up with a better estimate by looking at the size of aircraft and speed of flight you want, and base your estimate on producing roughly the same power as some existing aircraft in that size/speed range. Likewise, you can find the minimum takeoff for that aircraft, then add the length of powered flight you want to support, and use that to get a better estimate of how much compressed air you'll need.
In the end, my guess is that yes, it's possible as long as you set your goals low enough--carrying virtually no payload, and a powered-flight distance that's probably better measured in feet/meters than in anything like kilometers/miles.