This ability has an “intervening ‘if’ clause.” That means (1) the ability triggers only if you have exactly 1 life as your upkeep begins, and (2) the ability does nothing if your life total is anything other than 1 by the time it resolves.

In a Two-Headed Giant game, anything that cares about your life total checks your team’s life total. You’ll win the game if your team has exactly 1 life.