Not unless the missile was equipped with a transponder. You have to realize modern air traffic control radar is more of a cooperative link, not the traditional "skin paint" radar that receives an echo directly. Aircraft transmit codes when queried by the radar that ID them, altitude, speed, etc. The radar itself is rather weak.
But you can bet every single ATC in the tower at LAX had a visual on this, not to mention every westbound aircraft on approach out to 100 miles, not to mention all AC taking off and heading towards the loop eastbound.
Humm. Didn’t LAX have a phantom blip on a radar a few years ago that got everyone excited?