It makes no sense...
It's batted away quite neatly in the dialogue in the movie but the idea that all those planes could be held in a pattern by a phony ATC/Tower is preposterous. As soon as the tower got taken over there were still dozens of ways that the word could have gotten out from the airport. And as soon as one or two planes got the word it could have been relayed to all planes before there was any danger of them being brought down by the terrorists.
And what about the crews in the planes already on the ground. There was nothing stopping them from broadcasting to all the planes in the pattern about what was happening at the airport.
The antenna being blown up would have been spotted by at least one plane also.