Eventually will set Gmail addresses to forward, but didn't want to rush that so I remember to just make stuff not go to Gmail.
When I did this (from @gmail to @mydoman on google apps), I set up a filter to star/label anything forwarded from the old address, so I'd see an update was needed at the sending service/person. Perhaps the same could be done with FastMail.
It definitely can, but I feel that if I make it easy to automatically handle email on my old address at my new address, I'll get lazy about actually changing it. So I'll wait a bit to do that until most of my email is properly changed over.