Yes, the carbocation is a strong Lewis acid due to being highly electron deficient and bearing a formal positive charge - this is the second step of the reaction I described in my previous post. Water acts as a Lewis base due to the lone pair of electrons.
If you are asking if water will act as a Bronsted-Lowry base with a carbocation - that is not a reaction I have heard of. I guess theoretically it could be done, but most mechanisms simply proceed with nucleophilic attack by water.
I don't know what "Would it just be the case with alkenes and alkynes regarding to the pi orbitals?" means.