I don't think they will fit.
The folded over bit of leather is too thick to fit behind the metal bar over the stud the clips have to clip on to.
Maybe the clips will fit, so if you take them off the strap and put them on a better one?
QG- re-reading this, I'm confused. At first I thought you meant the folded bit of leather would cause interference with the hood, but now I see what you're talking about.
But the older type ofRollei strap lug, which was a slot with a stud underneath, (as on my 2.8C) doesn't use the alligator-clip style strap. It uses a strap which threads through the slot and buttons/keyholes onto the stud beneath the slot. (You could also just use a strap which attaches to this slot by threading around it in the standard camera-strap fashion, and foregoing the stud, as I'm currently doing...)
The alligator-clip style (as on my 2,8E) has only a slot, which has a small post/crossbar arrangement inside it; the spring clip snaps shut around when you insert the strap end. There is no stud below the slot on this model. The strap in this case never goes through the slot; only the clip does, and to about half of its overall length at that. There's no way to thread the strap into the slot at all, much less so deep that the folded portion of the strap could be a hinderance.
I thought the many Rolleiflex and -cord models were confusing (and they are), but the question which strap fits what model appears (at least to me) to be impossible to answer.
Rollei Club has a good page that helps a lot to identify a particular type of camera, and i would be great if a similar page existed that first describes/shows the different types of clips and straps, and then lists what strap will fit what camera.
The earlier types with the stud seem to take either the proper metal clips shown in that thread or a button-through-slit type arrangement, where the strap material itself interfaces with the stud. The later ones (E and later, I think?) take the alligator clips. And there are infinite ways to rig either of them to your fancy, too...or alternates like Gordy's thread attachments, etc.
For my "new" Rolleiflex 3.5F, I have simply tied a small loop (about 2 to 3 cm in diameter) of old bootlace through each strap lug. I then attach any of my other straps that have clips. The clips can be attached to the loops either by letting the loops come straight up from the strap lugs, or by bringing the loops down through the strap lugs and then back up around the edges of the lugs. The latter keeps the metal clips farther from the prism (or WLF on most), protecting the black finish. It works well so far, though I do want to "upgrade" to a tougher type of cord (nylon or something similar).
2F, 550/"parachute" cord works nicely for that. I recommend a loop made with a double-fisherman's knot...or, if you prefer, pull the core cords out of the mantle and use the mantle only with a tight square knot.