No. I have this enabled and Github closes my connections after a very short period. I use it primarily for SSHing into my cluster of EC2 instances (which does massively speed things up).
(ssh -fqN -o "StrictHostKeyChecking no" git@bitbucket.org >&/dev/null &)
with bitbucket and github in my zshrc and bitbucket stays open but github is getting closed at some point. It used to stay open however.