Extremely unlikely except in an unusual circumstance such as, the pigeon had been wandering around on soil which just happened to be contaminated by some undesirable organism, and something had just happened to have been transferred to its feet.
I get occasional scratches from claws in our aviary, as a pigeon doesn't quite avoid me in flight, with no ill effects. If it drew blood I would just put an antiseptic gel or cream on as a matter of course; I do the same if one of the kittens scratches me, even though she is indoor only. I'd do the same if it were human finger nail scratches (maybe even more so ).
Everytime I go to the loft, I come away with scratches. My arms look like some wild cat got hold of me. (LOL) My birds are very friendly to me and land on my arms, head, shoulders, anywhere they want. I have trouble cleaning the loft and shooing birds off my head. I just put a little anticeptic on them and go about my business. George
I have been scratched up so many times that I ended up expecting it. And I am still alive! In fact one of the birds used my head as a launching post and I ended up with a permanent scar on my forehead. Another bird did it and I scratch the side of my face. Obviously wash up after you get scratch. It is just common sense. You know if you scratch yourself you can self-infect, right?
Conclusion: pigeon scratch is safe. I am more worried about mosquitoes!