My .02 as a middle aged suburban white kid that grew up in Cobb County, but the Bankhead part of Cobb County is yes. It is a necessity.
An authority figure you can relate to, and that goes beyond the Xs and Os. I wish I could say we live in this great society race, religion, or gender never matters. People first is all that matters and the rest is just details. But we are not there yet. Without a doubt in my mind the greatest athlete of my time is Bo Jackson. A great person to look up to. Humble. Overcame stuttering which can be crippling to yourself if you let it. If I had a son, and he asked me who he should look up to, Bo would be on the top of the list. Not everyone is like that though. I think of a football team as a business. The coaches run the business. The athletes are the customers. In today's world, if you do not have a management team that reflects the customer base you want to attract, you are making it harder on yourself. There is a sizable segment of every breakdown of population that would rather deal with someone they feel they can relate to. I think you have to have a mix.
Given the media state we live in. Let say you have an all white staff, and some racial things happen on the team. White kids intimidating the black kids. N word gets used. You have set your staff up to be fired as soon as someone says they came to a coach and nothing got resolved. It is a black eye a university doesn't need. And for common sense reasons... there are at least 15 paid coaching positions on most FBS teams from head coach to strength and conditioning. 63% of the US population is non-Hispanic caucasian, 17% Black, 13% Hispanic, and then a mix of the rest. With the color lines being broken in the NFL 70 years ago, and the majority of college football athletes today being black... I'd believe you'd be setting your school up for scrutiny if the best candidate for at least three of those 15 positions wasn't a black hire. Not because of affirmative action, but because of the law of averages between the population breakdown, and the people who have played.
Blacks gain majority of college football rosters
So my personal answer is definitely, but not because kids will feel more comfortable, but because I believe it would be impossible to have the best possible coaching roster without African-American coaches on it and multiple at that.