WI: Władysław IV Vasa became Tsar of Russia

What happens if Sigismund III of Poland agrees to the compromise in 1609 and lets Władysław IV become Tsar of Russia, instead of trying to take the throne himself?
 
For one thing, that will take a complete turn 180 on Siggy's attitude towards Orthodox Christianity in general since he wanted to Catholicize Russia, which in itself is impossible.
 
Top