How would things have changed if Sansa had revealed her identity to Yohn Royce after Lysa’s death as opposed to before it, and why?

If it’s before, Sansa’s identity plays right into Bronze Yohn’s efforts to “deman[d] that I call my banners and go to war.” Here is a Stark at hand, a symbol to rally around, a fair and noble lady who can tell everyone about how Joffrey and Cersei are monsters and murderers – as Bronze Yohn whispers about how all of this proves that Jon Arryn was murdered by the Lannisters – and plead with the upright and honorable lords of the Vale to help her retake her inheritance from the treacherous Boltons and then topple the evil Lannisters once and for all. 

If it’s after, it’s complicated by the fact that she’s now both a witness and a suspect in the murder of Lysa Arryn, and that she’s under the protection and lock and key of Petyr Baelish. Now it becomes about Petyr Baelish the murderous Svengali, the man who murders his wives and kidnaps fair maidens as part of his corrupt agenda, and so on.