On a related note, how common is Mandarin amoung paleontologists (excluding, obviously, researchers from places like China)?
Not at all.
It seems like with all the fossils coming out of there, it'd be a big advantage to speak it,
Oh yes.
but I get the impression, and perhaps I am wrong, that even many people who work on these things don't speak it.
Yep. The limiting factor for learning it to a useful level isn't _speaking_ it*, but writing and reading it -- and, well, to read a scientific paper in Mandarin, you need to know _several_ thousand characters. In order to learn them, you need to sit down every day and write a line of every character you know, or you'll very quickly forget all except the simplest ones. Not many scientists have that kind of time.
* The difficulties of the language itself are quite different from those of familiar European languages (all the way to Russian), but I don't think there are _more_ of them.
Or how common is Mongolian, for that matter, (again, outside of the Mongolian paleontologists, who've done great work).
Even they haven't published in Mongolian. It's all in Russian or English, occasionally with a Mongolian abstract.