Restoring Unencrypted Backups to a TDE Encrypted Database via RMAN?

We are researching Oracle TDE and have a few questions/concerns regarding the implications of encrypting existing databases.  Most of the documentation I've found only applies to encrypting new databases, or contains minimal info about migrating existing data.  Most prominently:

If we have a unencrypted database that is currently being backed up in that unencrypted state, and we implement TDE (Transparent Data Encryption), migrating ALL data to encrypted tablespaces, does that then render all of our previous backups useless? 

(ie. Can you restore a previously existing unencrypted backup to a newly encrypted database?)

If not, then there's a huge risk implementing encryption, since you lose the ability to restore to a date prior to the day you encrypted your tablespaces.