To be short...Yes and Yes. But, really, I have done Disney Transportation for Cape May, and your only other option would be to take a bbus to EPCOT and take another bus (which run from 7 am most days) or take a bus to DHS and take a boat to Cape May. That, my dear friend, is a hassle. Take your cab and go. You could walk to Epcot when you get out. You will be let through but nothing in WS will be open except for restaurants which offer breakfast, like Norway.
Have a GREAT trip!!!!