Signal syncs fine between my iPhone and MacBook. I don't actually understand how, but it does.
But if you don’t have both devices close by or if you’re setting up your iPhone as new due to some issues and the restore from an iCloud or iTunes backup, then you’re out of luck because Signal prevents its data from being backed up to iCloud and iTunes.
This gives us the guarantee of forward secrecy. When you pair a Signal app, it gets to know the current keys used to advance the ratchet. But, it cannot deduce keys used to encrypt prior messages. It can only decrypt future messages.