Quick takeover?
In the miniseries it is stated there are 3 dozen shuttles per landing bay with around 200 bays per ship, and 50 motherships around the world. So we're looking at about 36,000 shuttles, let's say for sake of discussion a third are skyfighters, we're talking about 12,000 fighters. In the first episode it's also stated planes aren't effective.
They would have been able to conquer us pretty swiftly by targeting military installations with the fighters, not counting the firepower of the motherships themselves. I know it's a movie, but from a tactical point of view it would have been more efficient than deception (and probably minimal loss of lives too)..
I've got better things to do tonight than die
-Springer TF:The Movie