Don't know about freezing, but you can dehydrate it. Was a not-a-big-hit with the one company that I know of that had it for sale several years ago, though. I didn't think it was that bad, but it did take a looong time to rehydrate and lost the crunch.
i try to dice my leftovers really small and put in a ziplock and freeze them, i've havent tried whole or slices .. i've read it makes the flavor stronger to freeze, but i dont notice .. i use my diced baggies and add to soups and stews .. never tried to defrost and then eat ..
You can chop it and freeze it for use in things where it's going to get soggy/soft anyhow, like soups. It's no good for eating plain though.
It can be dehydrated, but I've never had dehydrated celery in anything where it seemed like it was a good use of dehydrator space (tastes differ of course)