correct me if im wrong, but isnt Coopers one of those special beer that is meant to be bottle fermented, hence the yeast in the bottle? This suggests a few things to me:
1. Coopers should be drank from the bottle not from the tap.
2. if it is meant to be bottle fermented then surely the yeast imparts some flavour on the beer, so it shoudnt make any differance whether you mix the yeast up or not.
personaly i prefer Coopers out of a bottle, not from the tap. I dont mind the slight taste coopers yeast gives (sparkling more so than pale ale). Do I mix the yeast up from my own HB - No way, but then again mine is mostly dried crap yeast. If it was good yeast that imparted flavour then I probably would, ala Tangent's post.