Based on what I'm able to see inside of the hole in the back of the "pearl", it being semi-hollow, I lean towards imitation. But I am going to take your advice and pick up a long-wave UV light to have on hand for examining baubles and beads (no bangles). (y)
There are plenty of "pearl" jewelry items here, but I have not idea as to which may be real pearls.
I gently lifted up one of the pieces on the tray and this is the view from behind, to the best of my ability to capture a decent image of it. And they are definitely glued in place.
OOF! That sounds painful!! I'm getting sympathetic tooth pain just thinking about it!! I'm going to try to get some high resolution closeups and see if I can give you a better look.
I thought it might be some type of salesman's sample array for potential buyers. The box is definitely manufactured for that purpose, very well made, and not a thing that could be easily whipped up at home at that time. The pearls appear to be permanently attached to that backing board through...
My grandmother worked as an assembler for a jewelry company in NYC from the mid-1930s through WW 2. Going through box after box in my 145 year old "attic that time forgot" (the family home), I found this 14" X 8" tray which I imagine is some type of company sampler of various types of designs...