You mean attach your Rpi4 via a 2x20 ribbon cable instead of directly to the hat hacker? Yeah, I imagine that should work fine. Main concern would be voltage drop, if the cable is long, for the 5v if power is supplied from the pi-Stomp board barrel connector. Probably fine, but the pi is picky about getting it's 5v and many ribbon cables use super thin 28 AWG wire. Noise perhaps too because all those GPIO's become little broadcasting antennae. On the positive side you're getting that noisy pi away from the audio circuits, so...
In the pi-Stomp Core 4 layer sandwich, there is about 7mm between the top of the 3A+ SoC and the hat hacker. So the kits I sell come with 2 small 3.5mm tall heat sinks for the SoC and RAM.