Not sure, can you create enough pressure to stop blood flow with a belt? If so, I guess it would.
Well ... maybe. If a belt is all you have, better than nothing. However, may be difficult to apply, and hold pressure, especially if applying to yourself one handed. A modern CAT-7 tourniquet can be applied more quickly and one handed (as in to yourself if necessary), and can be used for other purposes as well. Cost is about the same a a box of WWB 9 mm 100 rounds. Worth far more you need it!
without proper medical training, not sure I want to expose myself to potential liability with a complete stranger.
Agree. However, if it seems likely the stranger will die without treatment, and there is no one else to render aid, I'd very likely do what I could within the limits of the basic training I have. I carry a chest decompression needle in my med kit but this is for use by someone else on the scene who is trained to use it. Improper use possibly fatal. Another reason to have a basic med kit close at hand: for someone more qualified to use in the event no other med supplies available.
I keep a medkit bag in the trunk of my car,
Excellent! However, keep in mind that some gunshot wounds can result in bleeding to death in a minute or three. If a negligent discharge severs a femoral artery (think "Glock leg") you may not have time or be able to retrieve from your car. At many if not most indoor ranges, there are others who can probably render aid quickly. At an outdoor range, or in the woods on your own, maybe not.