A professional wont just guess if you have an alarm or not by looking for a flashing light. They'll come prepared either way, so the flashing light wont tell them any more then they already *should* expect. If they want your car they can get it, LED flashing or not.
I dont understand the concept of not having the LED. Every shit head that thinks they can break into a car, kick the dash and mess with some wires to get it started will be detered by the LED, they wont even think twice about it. Whereas if they dont think there is an alarm they'll smash the window and once the alarm sounds they'll go running.
That still leaves you with a smashed window.