What is the advantage to purchasing different portraits after your snippets are complete?

Yes, you can replace your avatar with other portraits you have gained at any time by tapping on your current avatar, then tapping on the pencil next to it. That is the only purpose for the portraits, and they do not provide any game advantage. While they can help differentiate players on a team, they are essentially just for fun to spend excess spending currency (i.e. Deja Vu tokens or drink tips).