I would not recommend it.
The drywall should be cut out just enough that the cut line will be hidden by the edge of the new stone going up, about 2" behind will work. Add blocking to carry the joint if the cut does not fall on a stud. It is highly unlikely it will not be on a stud. Set new cement board in place where the drywall was removed and use thinset to adhere the stone to the wall. Scratch a coat on the wall with a notched trowel and skim coat on the back of the stone before setting.