I can't get endermen to pick up grass blocks. I tested in a vanilla flat world with grass on top. Spawned 100 endermen and none of them picked up grass.
I waited about 5 minutes and would expect to see at least one with grass in their hand. I also tested this on a void world with just a grass platform so they couldn't teleport. I left that test for 20 minutes but no grass was missing.
This is version 1.12.2, tested with and without mods. The mobGriefing gamerule is set to the default of true.
I was hoping to use this as part of a modpack where you are forced to get a block of grass before silk touch is available. The weird thing is they seem to take grass blocks all the time and it's annoying. Now that I want them to take it they refuse to.
Edit: I've read that a piston can be used to push a grass block so I might use that as an option for the modpack instead.