You will in fact have the opposite problem! As the hair from your head ejects, the eyebrows will become bushier!!!!!
Aint't that the truth--for a while until I started clippering them back to a #3, I had a new possibility for a really ugly combover

. And I could get the sides w/ the growth from the ears

. Damn, I still have lots of hair, just not on top of my noggin anymore!