That's a good idea. Multi-use products thrill me. If my hair was still blonde, I would definitely use the blonde shampoo, but will stick to baby shampoo while I am a brunette!
I have recently started to swipe the brushes over an anti-bacterial wipe after each use, just to keep them even cleaner.
I can't verify any scientific validity to this, but it's my personal feeling that my brushes are cleaner for each use by doing this.