Turns out you can, thanks Wikipedia! They are not really olives, but they are loaded with lycopene, which is the same stuff in tomatoes that
Russian olives are a pesky invasive tree that is planted everywhere around Los Alamos as shade/windbreak, but unlike Chinese Elms which have no known use except for reproducing like mad and being impossible to eradicate, the Russian Olive is kind of edible.
I hopped the fence into my snowbird neighbors yard and picked a bunch of tiny mock olives from the tree. I put a few in my mouth, they were kind of delicious. They were sort of tannin tasting, but had a bit of sweet to them, not too dissimilar to fresh dates that have the skin you should peel, but are too lazy to do so...
They are probably much lower on the desirability scale than any of the bountiful crab apple trees in the neighborhood, but they are edible right off the tree, which makes them more desirable than, say, juniper berries...
Apparently there are much more delicious mock olives from the similarly invasive relative Autumn Olive tree which grows in the east. But these are not terrible, I may raid the neighbors yard some more for some low reward snacking. I am not sure if I can actually get enough flesh off these little pitted fruits to do anything with them, but they are not unpleasant. In fact, I think the more shrively ones are almost tasty! The firm ones are a bit bitter.
So there you have it, the Russian Olive:
Not really olives, somewhat tasty, mostly pits.