I saw the episode where Fry went back in time and had a relationship with his grandmother(Roswell that Ends Well). They say that Fry would be his own grandfather but the fact is that Fry would cease to exist since originally he came from his grandfather, Enos. If Fry did have a child with his grandmother, Mildred, then it would just be another child but it wouldn't be Yancy,Sr since Yancy,Sr is the direct son of Enos and Mildred and Fry's Biological Father. Also Fry wouldn't have his brother Yancy, Jr nor would the Professor exist since he came from Yancy,Jr's ancestry. Fry's new son who was meant to be in the place of Yancy would be another person and if Fry's son got lucky to meet who would be Mrs.Fry, then it still wouldn't produce Philip J Fry, keeping him out of existence.
Actually fry couldn't have impregnated his grandmother. He would not have existed in order to go back in time to do that in the first place. Plus its a cartoon that sacrifices "possible" for funny. Anyways What KingD19 said is possible BUT in a later episode Fry being his own Grandfather is specif to the story.
Yeah. The only way it's possible is what I said(I believe), but like you said, Fry had the Beta Brainwave, making him the only one(and the Chosen One) capable of fighting the Brainspawn because of him being his own grandpa. And it was brought up a few other times as well.