That's how mine works. The sparge arm is simply a copper ring with holes in the bottom .just above the mash bed. The HLT and MT have quick disconnects on the drain valve so you can feed to the coil then out back to the MT then for the sparge switch to a line directly from the HLT.
My system also has a float switch so you can turn on the sparge and it will shut off the pump when the MT gets too full and a temp switch so you can set the desired temp and it will shut off the pump there.
I'll be honest though, it's faster with my system to turn the MT burner back and either stir to prevent scorching and/or recirculate with the burner on. To raise the temp just recirculating through the coil seems to take for forever. One reason I almost never do step mashes.