I think if you do what you are suggesting, you'll end up with a fairly uneven wall. And unless you paint it w/flat paint, you'll see all the unevenness.
I suggest you take it off and go right to the studs and install drywall. Either that, or frame up a cripple wall in front of the stucco wall and then drywall. Of course, your room will be that much more narrower in my latter suggestion. (I'd do the 1st suggestion.)
IF you do the demolition, that's a good time to run wires to the 2nd floor (or attic or wherever), install new outlets, check the insulation, and put in new phone, speaker, and cable jacks while the wall is 'exposed'.