Yes. It includes most of the standard vim text objects, as well as providing an api for you to write your own. It also has the usual motions, plus an api to add your own. There are existing extensions for the more common vim plugin-provided motions as well.

While I don't know if it has programmable text objects, it does have the standard Vim ones from what I've seen last time I tried it.

Just checked the docs: Not only does it include text objects, you can write your own, if you don't mind getting your hands dirty with some elisp.