If the internal girts are reachable, then yes you want to attach the ends of the two walls to them. Then the two walls together where they meet, with a king stud or california corner. Double top plate going the other way over the corner. You may not need adhesive under the bottom plate, just anchor the walls, like with tapcons, extra anchors near the door(s). You will want a vapor barrier under the bottom plates, zip tape or a roll of foam, something.
Be sure to measure drift in the floor so your top plates are level, not all the studs may be the same height.