If we hear better from one ear, why don't we hear equal timed L & R signals in headphones from only one side?

Interaural time differences account for our ability to detect if a sound is coming from the left or the right. Amplitude differences between the right and left do as well, and can compensate for ITD. If a person has slight hearing trouble in only one ear, would they only hear a balanced headphone signal as coming from one side?