Whether they perform better probably depends on how the team felt about Wade. If he was truly seen as what was holding the team back, then you might see a big improvement on the field just from the positivity of having him gone. If on the other hand, the Cowboys problems go far beyond the head coach (and I think they do), a head coaching change, as you hinted, ain't going to fix this broken down train.
There a rumblings that many players don't like Garrett.
I know it's PFT so we must take it with a grain of salt, I just can't imagine how the players didn't like Wade Phillips. He may be a poor HC, but he has always appeared to be a likable guy. Not to mention, the offense has been outright bad! That is on Garrett, so who knows?
I know the Cowgirls are pretty bad, but there is a scenario playing out here to give Garrett a good name going into his 1st game as coach, their defensive line against a beat up offensive line for the Gnats. The Gnats are likely to be without Diehl and O'Hara. Will this make much of a difference? It all depends.
Do the players really dislike Garrett? If so, they will likely not get pumped for the divisional rivalry.
Will the Gnats O-line be ready? If not, Ware, Ratliff and that D-line could rattle Eli, who I might add has been great lately because of the time he has in the pocket.
And can John Kitna get the ball out quick enough before the Gnats defensive line crushes him! Their best bet would to be to try to get their run game going.
The only reason I give this game to the Giants is because Jason Garrett does not seem to play to the opponents weaknesses. He will likely try to pass against the Gnats and he will get Kitna crushed!