Both had their own offensive philosophies prior to Trinity, Beatty the run and shoot, Cov well, check out a copy of "The Bunch Attack". They joined forces in 2000 and their systems intertwined. It has evolved over the years, incorporating concepts learned from all levels of football. If i had to give it a name it would be a "pro-style-spread".
Coverdale should get a lot of credit for evolving the offense and the play calling (Along with some very gifted assistants who are outstanding teachers of the game), but make no mistake, Beatty sets the tone for the Trinity football program!
As to the thread title, I cannot see Beatty joining the WKU staff. I could be wrong, but at this stage in his life/career, I don't see him pounding the southeast recruiting trail and working the late hours that Petrino will most certainly demand.