Alas, no. Jackalopes are rodentia, and are most closely related to the wolpertinger of Bavaria, although the wolpertinger is winged, whereas the Jackalope is not.

As an aside to the decidedly cryptozoological bent I have been demonstrating, the Jackalope and the wolpertinger both have some basis in fact, as hares and rabbits can develop viral bone tumors in their skulls, which manifest as apparent horns! Just goes to show, non?