My Dog Swallowed A Plastic Eye From A Stuffed Animal. Will It Pass Through?

Monitor his/her situation for a few days, especially the stools. If the plastic eye is quiet small it should pass through with no problems.
If the plastic eye is not out or he's showing signs of paleness and lacklustre. Get him to a vet immediately. it might require an operation.

Yeah, it will probably pass through, but if he starts vomiting or eating grass you might want to take him to the vet.