Can Shrek take the ring to Mordor?

title.

Shrek is tasked by Farquaad to retrieve the One Ring for him. They, through reasons I can't bullshit through, are convinced the proper course of act is to destroy it in the fires of Mt. Doom.

Their first task is to resist it's temptation, and secondly to make it from Far Far Away (for our purposes, located geographically on top of the shire) to Mordor.

Can he and Donkey succeed, and defeat Sauron?

-For this task, he does not have continued support from allies such as Fiona, Puss, the Dragon, etc.

-He has no previous relationship with the Dwarves, Elves, or Gandalf, but they still exist in the world, and may aid or hinder their quest.

-He is still obviously a non-human monster in the world of Middle Earth, and will be treated as such on first look. Shrek behaves normally, and isn't bound to Sauron by any means.