The next show-runner could easily decide to bring any of the characters back, provided the actors are willing.
Actually, since the writers who create the characters own those characters, they need the writers permission as well. For example, a writer might want to bring Captain Jack back, and John Barrowman could even be available, but unless RTD gives his consent it won't happen. Likewise, anyone wanting to use River or the Paternoster Gang will need Moffat's approval.