That is a good point, his Grandma would have sure taken advantage of the situation. And it might have given Neville some confidence. Of course
Snape didn't have a thing for Alice so he probably wouldn't have helped. So Alice probably wouldn't have been given the chance to live. Unless Wormtail had a thing for her and asked, but I doubt if the Longbottoms would have made him a secret keeper, I suppose you could make Barty Crouch the secret-keeper for them though.
This is kind of fun lol