Yes it does maximize it chances. But the University of Texas, up until 2 years ago, essentially lapped every other program in the country in terms of profitability for the better part of the last three plus decades. If you put Saban or Meyer there, they likely have six or seven national championships at the least.
Mack Brown may not have been a corch there but he is a massive, massive underachiever. The fact that he's won a championship is irrelevant. Les Miles has won a championship too and I don't think many people would put him in the conversation of good HCs nowadays.
Corches lose games they shouldn't. UNC shouldnt get beaten by FSU twice. Any coach that loses to the FSU teams of the last two years is suspect. Unless you have a good explanation for UNC losing the FSU twice, Brown is proving to be a corch at UNC (similarly Cristobal losing to a 1 win Oregon State team put him on corch watch as well)