You can directly share your Apple Pages .page files with colleagues.
The corresponding EndNote library (or libraries) must be available and open in order to add citations.
If you are working on a single paper and moving between different computers, keep a copy of your reference library with your paper. That way you will always access the same library when inserting citations.
If you are inserting citations on only one machine, it is fine to move the document itself to other machines—as long as you will be accessing the document with the same version of Pages.
You cannot insert citations in your Pages document unless the associated EndNote library is open.