that's quite true for hearing babies. For deaf babies, being able to learn spoken morphemes and phonemes is much more diffiult. ASL has morphemes and phonmes. I must confess here that I've forgotten what they are but I recall it was much easier for me to understand what ASL morphemes and phonemes are than what the English ones are and I'm more fluent in English than ASL.
Phonics have never worked well for the majority of deaf - myself included. Speaking for myself, I must have a visual symbol for a spoken sound otherwise the sound will have no meaning to me. Other deaf don't even use sounds.
that's where the language delays can start because the parent is trying to make the child fit the mode when they should be much more concerned about being able to communicate with the child; communication is vital for the deaf.
However, no one here expects the parents to be native ASL speakers and most never become very fluent. As for periphreal exposure, a partial soultion is to enroll the child in a signing program (preferably local but this isn't always feasiable) with deaf adults and children. Even if the parents aren't as fluent in sign as the child, the child will be able to pick up on the differnces between the signing parents and the native signers and they'll do as the native signers do and when they're at home, they'll sign differetly.