You could try, but IME it's usually the pump filters blocked with algae. OE BMW screen-wash doesn't seem to mix with any other brand and then the filters get blocked by gunge.
I've had to remove the reservoir for a flush and the pump filters for a clean with a toothbrush on an E46 3 Series and an E86 Z4 which is an easy job as the reservoirs are under the bonnet.
Sadly I think the reservoir on the E89 is in the driver's side front wing behind the wheel-arch liner!