Well seeing as they didn't want Waterloo depot when they purchased YT, selling it to Centrebus, then I highly doubt it. What makes you think that Stagecoach fancy competing with First in West Yorkshire?
Gotta feel a bit for the longer serving staff at Waterloo, having been with Tracky who were purchased by Stagecoach. No real change but then to Centrebus, then to Yorkshire Tiger, and then to Transdev. However, it was always a bit of an outpost with Tracky. It was opportunistic for Centrebus but with Yorkshire Tiger, it seemed to be one of those activities that were entered into with great hope but soon began to suffer from lack of managerial focus.
@Andyh82 has called it right enough.... a mere stepping stone to some and an incumbrance to others
If it were First, people would be (rightly) calling them out for it but Arriva have a lot of form for similar purchases (see Chase Bus, TGM/Classic)