OK, I'm not a mechanical engineer either and I haven't done any fiberglass work. So why am I even writing about this? Feel free to ignore me.
If the fiberglass is done the way I've read then the first layer of epoxy will penetrate the cardboard fibers a little, including into the outer layer seems, and lock it all together. A straight circular column is really quite strong assuming it doesn't buckle. I think a 12" diameter, thick walled spiral wound cardboard tube with a layer of laminating epoxy is not going to buckle under a 165 lb load that's well centered. Yes, I'd stand under it. If I had a reason to, not just for giggles.
If the fiberglass is thick enough to take all the flight loads, the sonatube made a hand form and doesn't weigh enough to bother removing.
Internal structure? I'm not even going to gue... yes I am. I'm not aware of others doing it. I guess it would help prevent buckling, which I already guessed won't be a problem. So my guess is you don't need it.