I've heard of some guys doing that...and once I thought about trying it when I was pissed at how the cymbals were trashing the drum sound...but then I just 1. got the right/better cymbals for recording and 2. moved them to strategic locations in the kit setup...which is one of the things my drummer and I debated about, as he was use to having the cymbals where he plays them on his kit for live gigs...and I had them spread wide to the sides rather then any in the middle.
He's now use to my cymbal positions once he played the kit a few times.
Anyway...
Most drummers hit cymbals WITHIN the context of their drumming.
When you remove the cymbals...they will just keep hitting the drums, unless you can get them to "make believe" hit cymbals...and then add them later in those holes...which can be a PITA.
Yeah...you can leave the cymbals out for him to hit and just cover/mute them...but if you can get them set in balance with the rest of the kit...then it's more natural for the drummer.
AFA leaving out the HHat and then adding it latter...mmmmmmmmm...that might be even tougher, as the HHat is a BIG part of the basic beat on most stuff. Cymbals are just for fills and accents.
I did the same thing with the HHat...got the mic setup to where the HHat is in the mix, but I never mic it directly, and it's never rude.
Any drummers here that have done that...played w/o HHat or cymbals...and then added them later?