You can run an impact off a pancake compressor all day. You can run a cutoff wheel or 90 degree grinder with a Rolock wheel for cleaning gasket surfaces but it will die out quick. Expect 2-3 recharges to get a gasket surface clean on anything but a tiny part. Dont think of wizzing out a whole panel with a pancake compressor or anything less than a 220V 60 or 80 gallon upright compressor.
Unless you are doing bodywork, the only air tools I would suggest for the shadetree hackjob home mechanic are a nice 1/2" drive impact and a 90 degree air grinder with a rolock wheel attachment. Anything else is more of a hassle and liability for the marginal time savings.
Don't underestimate the difference between good air tools and Harbor Freight specials. I run Ingersoll-Rand tools and wouldn't use anything else. Snap-On tools are also good. Good air tools run much more efficiently so you use less air to do the same work. The cheap air tools are really good at turning compressed air into noise and really bad at doing work. A $300 impact wrench may seem like a lot of money, but with proper care its a lifetime investment.
For the record, my $20 yard sale 25 gallon Craftsman compressor will run all 32 lugnuts off and back on my Dodge without needing a recharge using my IR 2135Ti rattle gun.
Have you looked at cordless impacts yet? You can get really nice 3/8" and 1/2" cordless impacts from DeWalt, Makita, and Snap-On. They will do 99% of the work of an air powered gun and don't need a compressor. I would argue that a cordless 3/8" impact is a better tool than an air powered 3/8" impact due to similar size, weight, and power without the need for a compressor, hose, line oiler, dryer, and so on.