@ddljohn-- I think so. I think you can follow a basic cucumber pickle recipe to pickle apple cucumbers. Although I'm not sure what the taste will be like.
I personally like apple cucumbers sauteed fresh like zucchini. But if you have a lot of the fruit, pickling will be a good way to preserve them. It's not a good idea to freeze apple cucumbers. They will become soggy when just as regular cucumbers.