Gaelyn

Yes.
Ever since the update above, "a player riding an elk, who uses a translocator, teleports both player and elk."

On anything before that update, you will have to push or guide the elk through the translocator; you will not be able to take it through while riding it, but you can still take it through.

And yeah, earthquakes aren't a thing, but if you are playing with sideways instability for soil/gravel/sand, there is always a chance that a landslide triggered by you or a mob buried it. If you aren't playing with that setting on, then there shouldn't be any way that the opening could have been buried.