does this mod support the Spidertron at all?

Nope, since the base mod does not affect the spidertron, neither does this one. You can use this mod if you only need to change the vanilla spidertron grid size. Spidertron Extended, which adds higher tier spidertrons, also has grid size settings for each tier.

In terms of compatible equipment, I believe neither this nor the base mod change what equipments are allowed, except for not allowing the new speed booster in it (which shouldn't change anything, since it still has access to exoskeleton equipments)

Was any additional functionality needed?

i just find that a bit odd that the spidertron specifically doesnt get support, but ill check out that mod, thanks!

I will admit that the line is a little blurry, but I don't exactly consider Spidertrons as "vehicles" in this context, as they are more autonomous robots that can be directed via remote, unlike standard vehicles that need to be piloted manually (or via remote view, but either way, non-autonomously).

The existence of another mod that can handle spidertron grid size also dissuades me from adding it to this one (again, especially considering the base mod doesn't affect the spidertron either)