I have your sister ship with the same dresser. In my Parts Fisch it is shown as one complete unit with only one part number. Probably built and installed as one piece at the factory.
Having said that, looking at mine, there is no backing behind the lower drawers. Looking behind the drawers, across the top back rear there is a 1x2 or 2x2 wood framing with screws that appear to go upwards into the upper unit lower wood. So it appears it was built as two parts and then assembled at some point. You could probably pull your drawers and remove those screws, disconnecting the lower and upper parts. I'm sure that the upper unit is also secured to the wall, perhaps at the top. Hopefully they didn't use some sort of adhesive to hold it in place.
So it's probably do-able but not something I've done.