So the thread title asks a completely different question than the OP. I'll give my thoughts on both.
Title question: being out of shape has some of the same root causes for a coach as the US population (70% of us are overweight, and half of those are obese): Rich foods, plentiful abundance for most, large portions at restaurants and fast food joints, etc. On top of those societal commonalities, college coaches have notoriously long work days most of the year. First things to give way when you're severely over-worked are (a) leisure, (b) family time, and (c) exercise. A lot of these coaches do very little but work and sleep 10 or 11 months of the year.
OP question: Probably. To some extent. For most kids. Picking a coach is kinda like anything else in life: you're supposed to stay focused on the professional attributes, but how you get along with the person, whether you enjoy being around them, those are going to weigh in, too. A coach who looks ripped probably usually has a 'likeability' advantage. Just human nature.