IIRC, you should have a ticket that allows "hopping" to use the Disney transportation that goes between parks (like the EPCOT to TTC monorail) and be an on-site resort guest to use the Disney transportation that serves the resorts and Downtown Disney/Pleasure Island.
That said, in my many, many trips to Disney, I've never been asked to show a ticket or Resort ID to use the Disney transportation system. While a CM may ask you to show one of the two in certain conditions (ultra crowded conditions or use of the MK resorts monorail after the MK is closed), I doubt you will have any problem at all. Many people take a monorail ride or enjoy one of the resort restaurants on their first evening.
Enjoy the trip!