I also have an 87 190D. I can confirm that the heating system will work without the pump. I've done this when the pump has shorted out (which makes the entire climate system shut down). Unplug and forget. The only reason I replaced mine is so that when I'm waiting in the car on the cold day, I can turn the ignition to on and bask in the residual heat that's left in the block. For that reason only, it's worth replacing.

And just for general info, the heater valve in your car doesn't regulate temperature. It's either all open or all closed. Temperature regulation is solely the function of the air blend flap in the top of the heater box.