Does a 350 with casting no 3970010 have a one piece rear main?

Yes, a 350 engine with casting number 3970010 typically features a one-piece rear main seal. This casting number corresponds to a later model small-block Chevy engine produced from 1986 to 1995, during which time the transition to a one-piece rear main seal design was implemented. If you're working on this engine, you can expect it to have the one-piece seal configuration.