Can a 4-length road ever be Longest Road in Settlers of Catan?
You lose longest road; by definition, none of you have a road with a length of at least 5.

From the rules:


  Set the “Longest Road” card aside if—after a longest road is broken—several players tie for the new longest road or no one has a 5+ segment road. The “Longest Road” card comes into play again when only 1 player has the longest road (of at least 5 road pieces).