No, you cannot have the Roon core on any Control4 gear. You would need to have a compatible Roon Core that meets the minimum specs listed on this page:
You would be controlling the Roon Zone, as in any zones visible inside the Roon app would be controllable from the Control4 interface. Typically, clients set up an HDMI output from a Core (Nucleus/ROCK/Dedicated PC) and feed that into a Control4 matrix and then have audio routes configured in Control4.
We have a free trial, so I’d get started with the current gear you have (PC or laptop with those specs), and you can always upgrade Core gear later once you found the solution works for you. If you need more time past the regular trial to test different hardware approaches, just let me know and I’ll ping our accounts team on your behalf