Yes. They stay at the original point of origin. I don’t even get the move option I normally get for followers (my character will emote to move, but no text shows that the turtle will move). Cats will get it, but they obviously won’t move to where you say. If I check the list, it says the turtle is still following. If I have another follower follow me, it says the turtle stopped following.
‘Tis a bummer. I got a level 20 turtle I’ll have to break bonds with since I know it won’t leave the area. It’s either that or trek across the land—and sea—by picking it up and placing it over and over until I get to the new base.