We haven't set any hard and fast rules on what type of wildlife can be found in the game, so you can easily say generic animals you'd find in a city proper can be in Asgard. Pigeons could be among those, but lmfao Leondardo! You are an inventor, get off your ass and teach your birds something, ffs.

If it's easier, you are totally clear to get a pigeon from this event instead. It's not problematic by any means.