Probably not. They do constantly have SS agents on the roof with shoulder lauched Surface to Air Missiles but that would probably be too little too late. Navy ships have a system to destroy incoming missiles (Aegis ?) I 'spect the White House might have a similar system.
Uhh, you can't hide an Aegis Radar. There would be a gigantic ugly box with the 4 flat panels of the radar on top of the White House or some nearby building.
Also, you can't have the radar turned on in an area like that. Simply being in front of the beam can kill a person, much less the effect on electrical and electronic equipment in a multiblock area around the WH.
There are plenty of Air Defense systems between the Stinger and Aegis and I suspect the WH may have some small battlefield-type missles beyond shoulder-fired ones.