Yes and no. You can clay bar at any time, it removes anything stuck on the surface. It does not remove any product on the paint. I use it after cut to make it easier on me, and in a resto you want to use it before any product build back happens. So yes you could start with it but the cut part of the process is going to remove a lot of what the clay bar would be making the job then easier for the clay bar and more importantly the user.
I'll have to check out his videos, I watched from where you had it marked and that is good info. The key to what I think he is leading to is get it right then have enough product on it to take the abuse so you don't have to work so hard to "Buff it out"
It's a pretty entertaining and informative series of videos. He even goes so far as to dance on the hood of his junk car to show the real damage and swirls, and how much you can expect to get out polishing it.