Out of morbid curiosity, I tabulated ATS data (1988-2023) using covers.com (regular season only).
There have been 25 blacks who have been NFL head coaches up to 2023 (plus one in 1921+), but 6 with less than 1 season.
Out of the 19 with a season or more, 8 have winning ATS records (>50%), just four (Tony Dungy, Brian Flores, Demeco Ryans, Mike Singletary) with profitable ATS (>52.38%), and the overall record (all 25) is 1084-1090-72 ATS (49.86%).
Five coaches have >= 12 seasons (Total of 1201 games, more than half of all games), T. Dungy, M. Tomlin. M. Lewis, D. Green, L. Smith. First 3 were 51.7% to 52.7% ATS, last 2 around 48.4% ATS.
In conclusion, no long-term statistical advantage seems to exist. As usual need to be selective in evaluating coaching.