If Felidar Sovereign enters the battlefield during my upkeep, will he trigger?
No, you will not win the game this turn.

This is because both abilities are triggered abilities with "At the beginning of your upkeep" as the trigger. But the Sovereign is in the graveyard at the beginning of your upkeep so it will not trigger, and after Sheoldred's ability resolves and the Sovereign is one the battlefield it is no longer the beginning of your upkeep so it will not trigger this turn.