I'm doing the same thing. The original undercoating...where it is....is sound as hard as a rock with clean paint. No reason to peel it off. I intend to undercoat everything after the primer and paint.
It is a great, motivating feeling having that out of the way. Like- "this thing is actually worth puting parts on now". I hope if I ever do another build, I am in a position to go rotiserie and blast everything.
I will never, NEVER do another car in this fashion...too old for it as it is! Hopefully this will be my last car resto and all the rest will be playing.
PS. I only read a few entries here, but great stuff! I'll be back for the rest of it some cold day this winter. As for now, it is nice out and my car is calling...