Does Alpha Centauri have an Oort Cloud?

Could you elaborate on the possibility of Alpha Centauri, a binary star system located in the constellation of Centaurus, possessing an Oort Cloud? An Oort Cloud, if present, would consist of icy bodies orbiting far from the central stars, similar to the one surrounding our own Solar System. Is there any evidence suggesting the existence of such a cloud around Alpha Centauri? Furthermore, what would be the implications for our understanding of planetary formation and dynamics if an Oort Cloud were discovered there?