Sure, a clasp like that could be placed on a cultured strand. The engraving work on the underside of the clasp is very finely done, I'd be surprised if the stone weren't diamond. Was the tongue of the clasp stamped at all, aside from the 32? The metal looks like platinum to me.
You really should send the stand to GIA to be tested (and the stone in the clasp as well). You could try candling some of the pearls in the strand and posting the photos for folks to weigh in on; I'd do a variety of sizes in the strand. If you search for "candling" the thread should come up.
I have an old strand of pearls from the same time period (1920's) that look very similar to yours, that came with an 18kt white gold and diamond clasp. I haven't gotten mine tested at GIA yet, but a reputable, high end antique jewelry dealer said she suspected the smaller pearls were naturals, for what it's worth. Who knows. Even if they're not natural pearls, it's still a very fine strand worth having appraised and restrung. If you do take them for appraisal, try to find a pearl specialist. Good luck.