I believe so. The core is to help in the recycling of the old parts, so that they dont go to waste, they will get rebuilt most likely and then sold as a rebuilt/remanufactured unit.
Kind of like getting $5 or so back on a new car battery for turning in your old one.
The same would apply to the starter or anything else with a core charge.
'92 300CE - Sold
2004 C240 - C7 Wheels
2015 ML350 - P1, Pano, Ash poplar wood, Sport Dinamica interior, Running Boards Keyless go.