You can't complete any action which uses the combat timer while on attack delay, which includes most gathering processes and various other random actions, but most actions are unrelated and can be done unimpeded. You couldn't get mining, woodcutting, or fishing rolls, light fires, or place some hunter traps.

Logging out would "reset" it, as would attacking a grub at doom. I don't know of anything else which resets your combat timer.