A quick search online has multiple sources calling it "edible, but of poorest quality."
I have a large banyan tree in my yard that I have yet to identify exactly (apparently there are about 800 different species of "banyan" tree) - not quite benghalensis, not quite aurea, not quite benjamina... nor exactly any other kind of ficus I have compared it to yet... but it has tiny purple-red fig that it drops in huge numbers, that are actually really good, sweet, with flavor that is a cross between a berry, a raisin, and a fig. I enjoy them, and they are a lot of free food, which I guess because it's not native here and the birds don't recognize it, the birds never touch, nor do iguanas or anyone else except some ants. They love growing out of the coral rocks here. I think it's closest to aurea, but the leaves and fruit are slightly different from pictures I have found.
Anyway, my point is, nobody would have pointed me toward that tree and said it's good to eat, and things I read online of the most similar species were not particularly encouraging. But nonetheless, this particular tree happens to produce fruit that I have not died from eating, that I think tastes pretty good. I find they are best when deeper in color and more purple, because that's when they are sweetest - and usually they have already dropped by then. So perhaps others who tried them only ate them off the tree less ripe, rather than off the ground? I assume they have decent nutritional value, too.
I wouldn't choose palmeri FOR its fruit, but if you want to grow it anyway, maybe you'll get lucky like me and decide that what fruit it makes is pretty decent as snack food, even if it's if not something you would go out of your way to buy in a store.
If you find raisins edible, I would think any overripe fig - even of the most "poor quality" - would be comparable.
