Felidar Sovereign's triggered ability checks to see if you have 40 or more life as your upkeep begins. If you don't, the ability won't trigger at all. If you do, the ability will check again as it tries to resolve. If you don't have 40 or more life at that time, the ability won't do anything.
In a Two-Headed Giant game, your life total is the same as your team's life total. As such, the ability triggers if your team has 40 or more life.