Do enlightened people still get bored?

I guess what I'm asking is, is it possible to eliminate boredom with the dharma?

I'm not enlightened, but I can confidently say the answer is no they don't. Try it yourself. Get bored, then examine the three characteristics in the experience of boredom. Actually, the experience of boredom is very interesting.

I'm not enlightened either and boredom doesn't last long with me. Getting interested in what your senses are registering now is always fresh.

A famous female buddhist whose name I have forgotten spent about ten years alone in a cave meditating. Upon return one of the things she said was that it was never boring.

That's the one Cave In The Snow is about, I think. Tenzin Palmo, I think. (Terrible book, but interesting person.)