It may help, since you already have the pump, I'd give it a try.. But before you plumb it in,, get some temperature readings from the exsisting setup.. get a temp reading on the inlet and outlet of the coal stove's coil.. with actual numbers to work with, any changes can be tracked, and won't be subjective..
You may want to install a ball valve on each side of the circulating pump. This makes for easy repairs in the future, and you can also use the ball valve to 'throttle down' the flow rate if you need to.
I love 'science projects'.. keep us posted on the before and after results.. Do you own a laser thermometer yet??