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?
From DaVinci Resolve System Requirements, in the “Resolve Minimum System Requirements FAQ” part:
... your GPU will determine if Resolve will run at all on your system ...
So yes, you need a GPU, and even not just any GPU.
From the same source:
It’s ALL About The GPU
Your GPU is everything! It is more important than your CPU or system RAM (both of which should be up to the task too).
DaVinci Resolve offloads intensive image processing to the GPU. It also employs YRGB 32-bit floating point processing for exceptional color precision.
Of course GPU cores matter, but GPU memory matters more when looking at minimum requirements .
512MB – Forget about it. 1GB – You’ll be okay with basic HD ProRes work, checking RAW files but avoid noise reduction and optical flow. 1.5GB – Approaching the absolute minimum to use Resolve with some level of complexity in HD. Noise reduction and optical flow will still be problematic. 2GB – A comfortable HD experience, limited 4K work. 4GB – Minimum for comfortable 4K work. 6GB – You can tackle pretty much everything a project is likely to require. 8GB+ – You can actually tackle everything any project is likely to require.
Bottom line, if you’re looking at a new system on a budget and you’re working mostly in HD, I’d recommend an absolute minimum of 2GB GPU memory, really 4GB is a more realistic minimum. Performance also depends on the resolution of your media, the resolution of your timeline and the codecs of the media you are using.
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.