That's how I've always done it - frankly, it never occurred to me to clean it beforehand. The grill is already hot so I just turn it up, close the lid for a few seconds, open it back up and scrape it to death.
I've never had this problem because when I'm done the surface has nothing on it but metal.
That said, those bristle brushes are very hard on my non-stainless steel grates and the coating is starting to chip off, so I'm replacing them this year and had planned on switching to a wood scraper -- this article pretty much sold me the rest of the way.
J/K, the real trick it to clean it after you're doing using it and not let the solids cool. I use a foil ball most of the time.