Can a player with 0 life use Soul Conduit to make their opponent lose instead?
No, unless the player has a "Cannot lose" effect in play, like Platinum Angel. 

When a player goes to 0 life, before priority is regained (and the player able to activate Soul Conduit), state-based actions are checked and the player loses the game. 

Even if the ability were on the stack, it doesn't resolve before state-based actions, again. (e.g. 1 life, activate Conduit, use Underworld Connections)