I could be wrong, but from what I understand, they are edible for wildlife, but not for humans.

One Green World offers 4 varieties right after the grapes, but makes no mention of edible properties of honeysuckle fruit. There are Web recipes.

If you're talking about the invasive Japanese honeysuckle vine, L.japonica, yes, I have tried them. Taste pretty nasty. Edible yes, tasty - absolutely not.
I guess birds, and probably deer, eat them, but can't imagine being able to do anything with/to them to make them into something a person would care to eat.

The 'honeyberry' type edible honeysuckles, like the ones Larry Gene mentioned are, based on all the first-hand reports I've read, overly hyped. They've been discussed on this forum on a number of occasions - I suspect those discussion threads are still active, if you'll search for them.