Whether Neat Video uses CPU or GPU is down to your settings in Neat Video - nothing to do with Resolve. In Neat Video you should open Tools -> Preferences -> Performance -> Optimize Settings and run a benchmark to confirm whether it is better to use CPU or GPU on your system:
Automatic Dirt Removal is a GPU accelerated effect, and will use lots of GPU plus a small amount of CPU.
Different effects use CPU or GPU according to how they are designed. Pretty much all Resolve effects (ResolveFX) will use GPU, with minimal CPU usage. GPU is the bottleneck for those.
Third party OFX depends on how that developer created them - some are mostly CPU, some are most GPU, some are a mix. And some, like Neat Video, allow you to choose.
As others have said, render cache doesn't affect this. Render cache is the process of writing the result of effects to disk, so that next time you play those frames, the effects don't have to run again (until you change something). The process of writing Render Cache frames will use a tiny amount of extra CPU, to encode those frames (unless you choose an Uncompressed render cache codec). But it is a very small amount, probably not even noticeable.