Add-ons provides functionality beyond what Google provides.
If a shared document is constructed using this new functionality, does the editor have complete access to the incremental functionality of the Add-on?
It depends on the add-on. Once it's enabled on the document all the document editors will see it on the Add-ons menu > Document add-on that there is one or more add-ons enabled on the document but the add-on might not have any custom menu shown to them.
To use an add-on one user should install it (this is done once by user) and enable the add-on on the document (or form, or slide or spreadsheet) (this is done once by document). Custom menus might be dynamic and menu options might depend on user properties or other stuff.
NOTE: This is assuming that this question is about editor add-ons. Workspace Add-ons have a different "lifecycle".