Chances are you would not. Eric is using that to his advantage when he wants to go unnoticed. He tells Taste of Country:
"We just went to the beach, and I was clean shaven before we went down there, and I wore my eye glasses the whole time. Nobody knew who I was...It’s cool for me to still be able to do the things that we do, by not wearing the hat and shades. But when the hat and shades come on, I can’t go anywhere."
So, if you think a clean shaven guy with glasses looks like somebody you may have seen before. That could be Eric Church creepin' around.