No. The signal from your receiver will be on the receiver and that is what the receiver will accept. Yes, a stray signal can cause you to lose control of your receiver but it's not going to damage servos. Have you ever turned on your receiver before the transmitter and have all of you servos "twitch" or "jump". This caused by stray signals Sometimes they just cause twitching, but they can also command your servo to move past it's limits and damage the servo. You have to remember that the receiver gets all of it's "commands" from the transmitter, which it then passes on to the servos. Without the transmitter on first the receiver doesn't know what to tell the servos, and any stray voltage in the receiver can actually be passed onto the servo as a command, which it will execute. Servos work by comparing their given position with the position that the receiver tells it to go to. When you move your stick to the right, the servo will move to the right until it matches what the transmitter/receiver tell it where it should be. This is an over simplification of how they work, but it gets the idea across. When you turn on your receiver first there is no signal from the transmitter telling it where to stop moving at, because of this servos can be damaged.

When I first started flying I though the same way as you did. I was a bit hard headed about doing it I didn't change my habits until I destroyed a $120 high torque servo. Now it's just another habit I do when I'm at the field.

Ken