Walls – Help! Drywall anchor doesn’t go through metal

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:

1. You can see things easier.
2. 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.
3. Your nails or screws will not be binding to anything for 1/2-3/4 of an inch.
4. 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.

I don't suppose you have a hammer drill? Tapcons! (my favorite concrete screws, you need 2", maybe 2.25") bushed out with 1" worth of washers. Make sure they're not home first ;) If you fall into a void after drilling into the 'concrete' they're probably cinder-blocks. If you then can't get the screws to bite, make the hole even bigger and use really long toggle bolts. If this is the case be prepared for having to do it both ways as some holes will be into the meat of the block and others into the voids.