I believe so. The powers that be, don't want to factor in the gory detail of how we got there...just that we got there. And, to some extent, I can't blame them. However, I would like them to factor in 3 seasons of missing the playoffs...
With that said, the smart thing to do would be to simply keep him. He's on contract for another year. If he does great again next year, then you extend, but only for 2 more years. If he doesn't like it, he can go elsewhere. Odds are he'll stay. It may cost a little more money...but it's probably negligible and one would hope he'd cut the Bears a bit of break since they did him up so well after the SB.
I personally want him gone regardless, but I'll be happy to deal with him if he wins the SB this year... Or at least makes a valiant run at it w/o stupid errors.