Memory might fail me, but under the current edition I think that Parma is taught just after you swear the oath, so no, it is not an initiation. HOWEVER; that is an extremely cool concept, so it might be worth it incorporating it into your saga background
It could be done by teaching the basics during apprenticeship, but not letting the apprentice get the last few crucial secrets before he has sword the code. Hence all magi start with Parma Magica 1. Since you can't very well teach and teach, without the last secret.
With AM5, the Parma became more formalized. Basically the apprentice is taught most of the ritual, but the last crucial part is withheld. During the apprenticeship it is part of the rules of apprentices that the Master extends his Parma over his apprentice, both to protect the apprentice and prevent the master and apprentice's Gifts from adversely affecting each other. Once the apprentice passes the Gauntlet and is offically a wizard the last bits are taught.
There's an example of this in my online game that I run here at Atlas.
There is, in the RAW, no technical reason why an apprentice can't be taught the complete Parma ritual at any time. Indeed it can be taught to any Gifted character at any time.
However, the social convention of The Order of Hermes is that the final key, which makes the Ability usable, is taught immediately after Gauntlet. So, sure while your magus could teach the apprentice the complete Parma early both he and the apprentice will be in big trouble if the tribunal finds out. Your magus will need a Very Good and Convincing Reason for his actions if he wants to avoid being marched.
As I think I've mentioned before, in our saga, my magus actually did teach his apprentice the Parma prior to completing her Gauntlet.
There's a widespread enemy loose in our saga, and rather than take the chance that the apprentice might be victimzed while she's out of my magus' sight, she learned the Parma.
I think there were a couple of other folks out there who said the same thing...and really, I can see a number of Tytalus magi either doing the same or effectively "stealing" the ritual from their masters. I'd imagine that Tytali expect it from their apprentices.
In my saga all of the apprentices have been taught the Parma quite soon, and the magi just made a pact not to mention it to outsiders. Of course, people will eventually learn of it, which is when the fun will begin.