Could they......?
Yes - for the reasons given.
Will they? No - because only one team has. Like someone said, "on any given Sunday".
The 1985 Bears were the greatest team ever...and they lost a game to an opponent that was PERFECTLY built to beat them...speedy receivers going against a good but not outstanding bears secondary (big hitters but not shut down cover guys), being thrown to a quarterback with a lightning release (thus avoiding the vicious Bears pass rush) who was protected by the best offense line in the game at that time (giving him just that much more time).
Those 85 Dolphins were good...but they weren't going to the Super Bowl. But...playing at home...fired up after a pep talk from the 72 Dolphins before the game....and built / configured as they were....well, it was no surprise (to me) that they won.
The 06 Bears will probably lose to the Pats...a quarterback with less than 16 NFL starts under his belt going against a Bill Belichick defense is a mismatch...and while the Pats will not run up the score against the Bears, Tom Brady is exactly the sort of gusty but calm and cool quarterback who will stay in the pocket and call the right play / make the right throw against a mean pass rush...and he won't get intimidated even when they bounce him around after the throw. Plus, the game is on the road, and the Pats still have LOTS of pride...it will be a "statement" game for them.
Pats 17, Bears 13
After losing that game and with the undefeated season no longer in question, they will also lose to the Rams on the road. The Rams are a good team, and even though the Bears are better, the Rams will be looking to prove they are one of the elite team as well (assuming they are still playing as well as they are now). Plus, the Bears weakness on defense (and this is a comparative statement) is that they still do not have a SHUT DOWN secondary...the corners and the safeties are good (very good against the run in fact) but not great...they rely on the pass rush. The Rams will be fired up, as will be their fans...the Bears will be on the road and thrown off because it is a Monday night game.
Rams 27, Bears 23
I still think they are the best team in the league though, and my current Super Bowl pick....