That engine HAS to go into a C8 Corvette, as them be the rules for the class they're racing in.
That being said, they're allowed to change the minor internal components. The C7.R is actually a de-stroked LT1 engine.
They may or may not increase the displacement in the C8 with the flat-plane crank. This style of crank produces more vibration, so a higher displacement will create more vibration in the car.
It might not go in the Z06, it might be reserved for the ZR1.
I'm sure the Z06 will have forced induction of some sort. It HAS to have more than 650hp as it's gotta have more than the C7 Z06. You're not going to get that kind of power out of a factory stock, naturally aspirated V8 engine.
Just my $0.02.