Well, after a fashion, yes, it should do. Even crushed rather than ground eggshells deter slugs and snails, the eggshells have sharp edges that they don't like, but in my experience, they're not that effective. If you grind them to a dusty mixture, then that will stick and dry out slugs and snails (they don't really like any surface that's sharp or very, very dry) and I can't see why it wouldn't work on beetles, directly applied. It's quite difficult to breath if you're heavily doused in powder, and in the case of beetles, it will work its way into any gaps between thorax and abdomen. I suspect you'd get the same results if you used talcum powder, which is just magnesium silicate with some perfume added. In other words, it's not the fact they're eggshells that counts, its that they're ground down into a fine and possibly slightly gritty dust, but it is one way of using up an otherwise waste product, unless you're someone who regularly crushes them a bit and puts them on the compost heap anyway. Using them as an organic pesticidal treatment sounds good, so long as you're around most of the time waiting to shower some unsuspecting beetle as soon as you spot one, but it's not going to work when you're not around other than for gastropods, and only then if you've applied a thick enough layer to prevent them reaching particular plants.
If you're trying to be organic and eco friendly, the use of an electric grinder needs to be taken into account - much more ecologically sound to add them to a compost heap.