Yes, under most circumstances. Aircraft taxis fine on one engine. As a matter of fact, with two engines running you have to ride the brakes quite a bit to keep it from accelerating. It also saves gas and mainline (who is paying for it) and the environmentalist love that.

Look, it's not that hard and as a CA you should know how long it will take you to taxi to the gate. Shut it down after cool down and wait to start the APU until you get within throwing distance to the gate. It spins up so quick it will be up and running by the time you set the brake.