During a MP match, the game state is always present on all clients. Essentially, all players run an ordinary SP game simultaneously, but receive the inputs from each other over the network. And each player simply "feeds" that input (received from the other players) into their own game instance and since the behavior of it is deterministic, all of the instances stay in sync. To be fully precise, it's not the mouse movement or button clicks that are shared over the network, but the game "commands" like moving or training units.
What the host does in addition to that is manage the network connections to the individual players and e.g. letting them know when someone disconnects. Therefore as soon as the host leaves, the clients are cut off from each other, can't communicate, and the match is closed for everybody.
With the proposed behavior, the disconnected player wouldn't lose anyway, as long as the other player(s) wait for him to come back.
Could work I think, but might not be necessary. The problematic case is when clients leave when they're about to lose... then it shouldn't take the host too long to finish it anyway since they were about to win already, no? Depends on the victory condition, though.