I have no problem hearing the alarm. I can't even have an "alarm", as I hit the roof when it comes on... just have the radio on low. I do have a dh who will wake me if I should sleep heavily, but I can't remember him ever having to.

And absolutely - if you can address the underlying issues, do.
When I get panicky about not sleeping, it helps a bit to reflect that that it's just an emotional reaction, and it will pass. I can function fine physically on little sleep, it just doesn't feel like it.