Maximum skill level?

I have just recently noticed that there is a MAX_SKILL field in the game (here). The nearby comment seems to imply that skills > 10 will perform identically to skills = 10.

Does this constant actually do anything? Should I turn off skill gains for level 10 skills to preserve focus? Or is this just a constant that does nothing in practice, letting skills (and benefits from those skills) increase arbitrarily high?

Yes. There are uses of it; it limits the max speed at which you can (un)install vehicle parts for example.
However, it’s not a hard cap if I understand that right. You might still profit from higher skill levels (with diminishing returns, of course) in different fields, like (currently) disarming traps and melee.

also the stat through skills mod keeps adding stats even past the 10 skill level