Is it possible to use DaVinci Resolve without any GPU AT ALL? I have some plan to get servers that are powered by Intel Atom C2750: Intel Atom® Processor C2750.

... and they don't have any GPU at all.

Is it possible to render at this CPU? Render time isn't the problem. Just ... is it even possible?
Even if you could tweak, say, your machine's BIOS or even Resolve's own settings to somehow not use any GPU at all, I really don't recommend doing it. Resolve is built around GPU power to render stuff.