I don't know of any sliding glass doors that are not new construction, I suppose you could cut the nailing fin off to make it a replacment if you really wanted to.

The wood in your pic thats not in good condition is the frame of the door and would be removed in a normal installation.

Weather the stucco will be damaged or not depends on how carefully or carelessly the removal of existing door is done.

look closley at the 2nd pic how the aluminum threshhold is directly underneath the 2x and at the wood shims beside it about 3" up off the floor and if you look really close you can see the endgrain of the sill plate behind the sheetrock with a stud sitting on top of it.

If that's dry rot I see at the bottom of your frame, its got to go, one way or another. A skilled carpenter (not a "door installer") could cut out the bad bottom section of the stud and replace it with minimal damage to the stucco, but that may be a moot issue. I'm replacing a slider in a stucco wall too and have found that you have to be very lucky to find door with a rough opening size that will just slip into to the old frame without a wide band of trim around the door. That will really be a negative for appearance so we're adding $400 to our budget to cover stucco repair. Most major window mfrs make patio doors in replacement sizes (Integrity does not) and the use of the nailing fin is preferred but optional. If not used, it's bent back out of the way or cut off.