I'll focus on a couple of things you pointed out in your post.
"Little cans" - which they are, and if you are just beginning I won't say don't do it, but would caution against it. It's kind of like the difference between buying a pint of milk at the grocery store or a whole gallon. You'll probably use the whole gallon, but maybe can't afford it. OK, that was kind of dumb on my part. If you can't afford a compressor, but want to try airbrushing, then I would say give it a shot, but you are still wasting money on the cans.
You can't refill them, they have no way to regulate pressure and as you use them, they condense and start to get cold. You can place the compressed air can in a bowl of warm water to combat the condensation which will help some.
I'm assuming you're looking at the kits that come with a simple suction feed (big jar on the bottom) single action airbrush. Those actually use a lot more air, since the air not only moves the paint through the brush (and nozzle) but also has to create the suction to bring the paint up from the jar, through the straw and through the brush.
If you are just beginning, I wouldn't say absolutely no, but you want to take a look at big picture stuff. Airbrushing isn't just pouring paint into a jar, hooking up some air and *poof* you have a flawless job on that kit. It takes some practice and some patience, and a LOT of trial and error. I think the trial and error part is where those little cans become VERY expensive, as you'll go through them quickly just learning how to use the airbrush.
Anyways, just my thoughts on the matter. And yes, many years ago, I did just that. Bought an Aztec airbrush and spent a fortune on those little compressed air cans. Found out that my airbrushing wasn't bad, but the more you use the cans, the lower the pressure gets, which means your paint needs to be thinner, etc. It's a vicious cycle man!