Unless something has changed, Google Groups aliases should always dynamically change permissions based on people's membership in the group.
The problem it sounds like you're having is that these docs aren't showing up in UserC's doc list. This is because UserC must first open the document before it will be added and remain in the doc list.
For a single file, you can just email the link of the doc to UserC, ask him to open it, and it will be added and available.
For multiple files I would suggest adding all of these to a shared folder so that once the folder is shared and accessed, all files will be up to date.
Another option for multiple files is to create a "Master List" of all admin docs that UserC will need to access. This could be a Spreadsheet or Doc that just has a list of links (and possibly descriptions of each file). You can then just email the link to that single doc to a new admin (UserD, E, F for example) and they will be able to have a single file that will house all relevant docs. As they click into each link these docs will be added to their doc list.