TL;DR: Don't do it or get a replacement thermal pad, _not_ thermal paste!
OK, I've just tried it, so here's the deal: The gap between the cooler and the chip is massive compared to the ones I've encountered on MSI X570 Tomahawk and X570 AORUS Pro, which really benefited from removing the thermal pad and replacing it with a good thermal paste.
Not so on the C8DH. Repasted it with enough paste, until it made contact (checked by attaching and detaching the heatsink).
Idle temps: 60-68°C and climbing (with zero fan GPU covering the whole thing)
That seemed a little high.
Just redid the setup and replaced the only slightly damaged original thermal pad: Idle temps: steady at 60-62°C