An airbrush 1) Does not care where its air comes from, and 2) Is a stupid piece of steel!
The problem with canned air is that the pressure drops as you use them. As they are used they get cold, and that temperature change causes the pressure to drop, which in turn lowers the airflow at your airbrush. As long as you can keep the pressure consistent and the air clean and dry, the airbrush really doesn't care where that air comes from. The fact that the air is coming from a can won't affect how thin a line you can paint except that, as noted, the pressure will begin to drop.
Airbrushes are stupid. They don't control the lines or anything else, they only do what they are told. The ability to paint a fine line comes as much (or more!) from the abilities of the user as it does the brush. My airbrushes can paint far finer lines than I am capable of doing.
To answer your question, sure it can be done. Swap out your air cans frequently and keep the pressure consistent, and practice, practice, practice!
There are, of course, alternatives to cans and compressors. There have been numerous posts on that subject, but the most common are air tanks that are used to inflate tires (about $30 plus the cost of a regulator and some associated plumbing) or a carbon dioxide or nitrogen tank (normally leased and I don't know the prices).