I would guess the West Yorks/GM cross border routes will be franchised by West Yorks, except the 184 already franchised by GM.
Whether cross border routes in GM are franchised seems to have been largely determined by which depot they run from (Except the 184 which I think might have been subsidised by GM). So if West Yorks is similar, the 587, 590/1/2, the 66 between Keighley and Skipton etc would be franchised.
Their relationship with the WYCA is basically irrelevant under franchising. The only thing that matters is is Transdev Blazefield capable of bidding lower than First, Arriva, Stagecoach, Go Ahead etc? First could be as obstructive as possible and WYCA would still give them every contract if they had the lowest bid.