I am taking care of a dog whose owners moved out and him left behind. To my knowledge, he has never had any shots.
Today, he treed a coon, and most racoons are tested positive for rabies.I did not see the racoon go at the dog, nor did I see a wound.
My question is, is it likely that he would need to be tested before getting a rabies shot? (or any other shot, for that matter)

Well, unfortunately, the only way to test for rabies is to be-head the animal and send it in for testing.
So, NO....don't have him tested first. If there was no contact between the two..he should be fine. If you are worried, the vet or local humane society will keep him under obsevation for a period of time for you, at a cost.
He needs to have his shots, not just rabies, but the whole series of shots...parvo and distemper shots are equally important.

Here's a good website you can visit to help you out a litte.

http://www.peteducation.com/