While a wooden bullet could be used to fire grenades, did they ever use a MG platform do it?
While I've learned to "never say never" when it comes to this kind of thing, I seriously doubt that they ever used a machine gun to fire rifle grenades. Simply because there is no evidence that any of the machine guns were ever fitted with the rifle grenade launching device. There was simply no point to doing so. if you've got rifle grenades, odds are really good somone handy has the rifle to fire them.
Likewise, I've never seen any information about any German MG that was fitted with a bayonet. Kind of pointless. pardon the pun.
The Japanese, on the other hand, DID have an LMG that took their rifle bayonet.
Would Be interesting if someone fired these into ballistic gel.
You can perhaps, find a modern equivalent in the W.German training ammo used during the 70s (no idea if it is still in use today).
7.62mm NATO, it was a plastic case which included the bullet, as one piece, attached to a brass case head (for function). When fired the plastic bullet tore off and went down the barrel at tremendous speed, 5,000 fps or so I heard. BUT, being very light (something like 17gr) it lost speed very rapidly (and accuracy was about zilch). We were told it was lethal to about 15 feet or so, so it wasn't harmless, but it wasn't dangerous at longer ranges. I did get told that if you got hit by one at 25m it hurt like a sumbitch...
but I have no personal experience with that.
A wooden bullet would be a little bit heavier, so wouldn't go quite as fast and would likely be dangerous a bit further out than the plastic ones. Fired into ballistic gel, I would expect very shallow penetration and very rapid veering off in some direction, assuming the wooden bullet didn't simply shatter immediately.