Mortise


Yes, you can disable timed re-lock if you wish.


Keybox


No, it lock immediately once the keybox is shut.


Deadbolt 01/02 & 2S


Yes, you can disable timed re-lock if you wish.


On the Deadbolt 02, if you have the door sensor installed, you can only disable the auto-lock by uninstalling the door sensor.


Latch


No, it locks immediately once the door is shut.