How does pressure influence the dehydration of salts? It's well known that the boiling point of a substance increases with pressure. I was wondering if something similar happens with hydrated salts and the temperature at which they dehydrate.

I mean, if the pressure is increased, does the temperature at which a salt dehydrates rise or is it not affected by the pressure?
Yes - the pressure will impact the dehydration temperature. 
You have correctly identified that temperature and pressure are related by the Gas laws.
High pressure can also force water molecules out, as water is loosely bonded in salts.