Not that I've found. Some brush HUDs stay "up" when a different image is selected (crop, retouch), but most do not.
I suggest assigning easy shortcuts to any of the Quick Brushes you use regularly, and launching them from the keyboard.
This is also an instance where a multi-button programable mouse could pay for itself. Assign those shortcuts to some of the mouse buttons. (I use and recommend the Razer Naga; surely there are others, and newer ones. The increased resolution alone is worth the price -- but all that is off topic.)