Will 340 HP manifolds fit 360 crate engine?

It's hard to say how much you will give up using manifolds vs a good header.
On a mild engine it will be little to nothing. On your 400hp, 360 it will be more.

On my 340 (fairly aggressive, high RPM build), I lost 13 mph and over 1 second in the 1/4 mile when I cut off my headers and went with 340 manifolds (other small changes were also made but most of the loss came from this exhaust change).