That's true, if you are a full time employee of the school you can be a head coach, and if you are a part-time employee I think you can be an assisstant coach. But unless you have solid pull at that school its a slippery slope to walk.
I read somewhere that the average stint for a Texas football coach is just four years, with a degree. If that degree is math or science the average jumps to seven years. If your title is maintenance or janitorial it is likely to be shorter, unless you have solid influence. So make the committment and do a four or five year course of study and get that extra job security.
If a degreed coach decides to pull up stakes and relocate the prospects are good to great that he will find a job. Otherwise, most likely fewer places to choose from. However. If you have a stud athlete or two, I mean a player with a reputation, or several kids who play, (here comes some exaggeration) your chances are as good as the math and science credentialed coach. Oooh, that's a controversial thing to say. My mother and dad would slap my mouth, or in this case my fingers for that.