Parece que a resposta oficial é "não".
Existe um relatório do Bugzilla de longa data que lhes pede para ativar esta funcionalidade. Com base nas discussões subsequentes nessa página, tentar sincronizar os cookies seria problemático:
Richard Newman [:rnewman]
It could be done, but I doubt we'd want to support it.
alex
why not? would be useful for many people. when its a problem with storage space on mozilla servers ... it would okay when its only supported on own sync-servers.
Richard Newman [:rnewman]
Nothing to do with space, and everything to do with potentially destroying your browsing experience. I have little confidence in being able to reconcile simultaneous changes to your Facebook session cookie, for example. That means data loss.
Gregory Szorc [:gps]
Cookie sync is not currently on the roadmap.