Can i leave existing drywall alone when adding two small walls to a finished basement?
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&amp;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.