My understanding is that at least originally, OSP would be destroyed in reflow. leaving you with bare copper. in that case you would paste the test points to stop them oxidising in the field... maybe there are different types of OSP that don't do this now?
I never paste ENIG test points, but you do need to be careful that your test points are not puncturing the pads and leaving room for oxidation to start. pasting them would probably help with that.
if anything, this discussion about one aspect of manufacturing becomes one more story about how EVERY part of a manufacturing process is related, and can be critically important, so you need to think of everything you are doing in context.