Will Skyrim work properly if mods and main files are split over two HDDs?

It's possible, but it could have serious impacts on performance - script lag, which is determined by many factors such as your PC specs, etc. However, it could work without problems at all, it just depends on the PC.

I recommend using 'Mod Organizer' (for Skyrim) to do this seamlessly. Just remember, it can have script lag, but it may also not have any at all. Good luck if you do try!

EDIT: This is just regarding your mention of Skyrim. Extrapolating from that, I assume all Bethesda games would work as such, but those are optimized for modding. Other games which are not so keen on optimal modding experiences will suffer script lag, or may not work at all.

Source: Personal experience on several PCs