Wedgies count. If it falls out and hits the ground before you retrieve it, it doesn't count.
The PDGA rulebook is a vague and mystifying thing, so there could be an argument about semantics.Not to argue with the all learned Three Putt, but there was a thread on the PDGA site that suggested that once the disc had come to rest the throw was completed so it wouldn't matter if the disc fell. I can't find the post now but the relevent question was about a disc hanging from the top ring. Since the ring isn't a catching device of the basket it isn't a completed hole. But what if a gust of wind came and blew the disc as you were walking up to it. And the answer is that if something moves a disc after it has come to rest it is to be returned to it's previous location. It defined "at rest" to consensus of the group. So it would seem that the idea of getting there before it falls is a myth if it is still moving you wait until it's done if it is done moving the hole is complete. I will look for the post cuz it had the pertinent ruls quoted if you find something that suggests I'm wrong just keep it to yourself. lol j/k
However, one of the enduring LMAO moments in disc golf is when a guy nails an approach from 100+ ft and it sticks in the side...there is the momentary smile, followed by the realization of his situation and the inevitable "Haul Ass" to the basket to grab it before it falls.
If they change that rule, they have no sense of humor.