bicycle=yes CAN be used on a highway=path, but it is not necessary as bicycle=yes is the default value for a highway=path.
"highway=path indicates a generic path that is used by pedestrians, small vehicles like bicycles, and/or animals. This includes walking and hiking trails, bike paths, horse and stock trails, mountain bike trails, as well as multi-use paths for cyclists and pedestrians or similar combinations."

See: https://wiki.openstreetmap.org/wiki/Tag:highway%3Dpath