You could but why would you?
You are going to have to mud/tape your corners whether you take the drywall out or not. It will take you no more than 10 mins to dremel or knife out those two tiny sections of drywall.
Why you should:
- You can see things easier.
- You aren't relying on drywall for wall structure. I know this wall shouldn't be supporting anything but any weight at all will crush drywall.
- Your nails or screws will not be binding to anything for 1/2-3/4 of an inch.
- You will not be able to frame really tight unless you crush the drywall.
Points 3&4 could lead to a wobbly wall. Think of taking a big couch down in this basement. Corner of couch hit door frame hard. You don't want the top moving.
There is a ton of information and history out there.
Studs are strong pieces that are the internal structure of your walls. They are covered by some type of material (the "skin") that is what you see when you look at a wall. If you imagine your wall without any type of skin material, there are probably two studs at the left and right edges and definitely two framing members (similar material as studs, but the term studs explicitly refers to the vertical members) going horizontally at the floor and ceiling forming a rectangle. This rectangle has many vertical studs inside of it, usually space at 16" or 24".
A term you'll see sometimes is 16" O.C. which means On Center; it just means the center-line between two studs is 16" apart and there is about 15.25" of air in between them.
Your studs are covered on both sides by something. These days it is typically drywall (sheetrock) which is cheaper and easier to install than most alternatives. Your surface could also be plaster, paneling, tile, etc.
You need to use a stud finder to locate where your studs are because you need to attach heavy objects to studs. Drywall can only support very little weight. To use a stud finder:
- Put masking tape horizontally on your wall.
- Place the stud finder against the wall, holding it vertical.
- Press and hold the button.
- Hold it still for the first half second so it can calibrate itself.
- Move the stud finder horizontally across the wall and mark on the tape where the signal is strong.
- If the signal acts weird, make sure you slide the stud finder sideways at the same height.
- Take a tape measure and try to find a pattern between your marks that is 16" or 24" apart.
- Now you can measure multiples of 16" or 24" and know where other studs are.
You need to determine if your stud are wood or steel because the type of fasteners (screws) you use depend on it.
There are other methods of determining this, but here's one: Figure out where your fasteners are going to go and drill a small pilot hole (smaller than the size of the fastener). If you get about a 1/2" deep and hear a terrible screeching noise followed by your drill bit sliding and having no resistance, you have steel studs. If you get 1" in and you start to see saw dust coming out of your pilot hole and your drill still feels like it's biting at something, you have wood studs.
If you have wood studs, you can use general construction screws (NOT drywall screws). If they are steel, you probably have to use toggle bolts. Toggle bolts are a pain to use, so you can try using self-tapping machine screws with a fine thread first. Make sure your fasteners are long enough.
There are many other types of walls out there so if things don't seem right, maybe they're not typical stud walls.
Best Answer
Hang a piece of 1/2" to 3/4" birch plywood (depending on how strong you need it to be), the same dimensions as the cabinet, on the wall, securing it with counter sunk #10 or larger screws, at the stud, and countersunk toggles at the corners.
Hang your cabinet from the plywood, and stain/paint the plywood to match.
If you don't want to see the plywood grain, you can cut it a little narrow, and glue hardwood edge banding to it, and then stain/paint to match.