It's possible. You need to let the pit dry out a little before you start carving. Depending on what you're doing a couple of days to a week. If you look up "avocado pit pendant" you can see some surprisingly intricate carvings. From what I've seen though people usually start off by making buttons. Like the kind you'd find on clothing. Once the carving is done you let it dry some more and then seal it like any other wood. Be warned though during either of the drying stages cracks can form or full on splits completely ruining the project.

There are a people who carve the pits. There are a bunch of pendants and jewelry and stuff available on Etsy.