Can pop rivets be used to mount windshield molding clips if for whatever reason you don't have anymore of the little nail heads left?

 

This is a bad idea for a couple of reasons. First, this area is a water seal. Drilling a hole for a rivet or screw is asking for a leak. Also note that a pop rivet has a hole in the middle of it. Second, if you use the more common aluminum pop rivets, that's just asking for galvanic corrosion to start rust all over again.

The bottom line is that the right way to fix this is to use a stud welder to put new anchor studs on the pinchweld.

 

I agree with Joe that's the right + best way to do it. There are screw studs commonly available. You drill, then screw a small post in that replaces the stud. They are very widely used, if you sealed each one you put in, they would probably last your lifetime...for recreational use of the car. They are dirt cheap, and you can do them yourself. Search ebay for window reveal studs.

 

Two very good posts
The area should be rust free and primed with epoxy.
I have used both with the screw in the area was primed with epoxy primer holes drilled and stud installed. Then seam sealer was used to seal the new stud and then the area was re primed and then painted.
Before the window tape went down the area was primed with a brush on pinch weld seam sealer that the glass shop used to seal and promote adhesion with the tape.
The key to long lasting work is detail and letting all products cure properly before the next step.

 

While I know that screws have been used successfully for a long time, after welding in new metal to repair pinchweld rust I have a REALLY tough time drilling holes into the new metal.

 

Ditto.
I had to deal with the same mind set, so I put a dab of "dum-dum"
on the backside of each clip around the screw hole before screwing the stud in.
After tightening the screw down, a little "dum-dum" oozed
around and through the clip which was easy to clean up.
I feel pretty good about the seal.
I've done this with multiple cars with no problems.
I wouldn't use pop rivets for all the same reasons that were previously mentioned.
I also repainted after installing the clips to cover any places
where paint was scarred during clip installation.