Nope.  Being a good head coach has nothing to do with knowing offense.  It has to do with knowing people.  Hiring good coaches, letting them coach, holding them accountable for results.  Bill Belichek doesn't know squat about offense, I bet he doesn't even tell them to run or throw on 4th and 1 - he just says "go get it" and holds the guys accountable for the result.  Harbaugh, Tomlin, Carroll, Rivera, Quinn - none are offensive type guys.  All have been in or won Super Bowls recently.  It's just like managers at work - they don't really have to even know how to do the job in many cases, they just need to know how to get the employees to do the job well.  One of the reason Fisher was so terrible was because he didn't let his coaches coach, so he couldn't get anyone of any talent to even interview.