No there’s no corelation between the user and mcebuddy running. MCEbuddy runs as a system service by default (unless someone manually changes it).
As a system service it doesn’t have access to user mapped drives as explained on this page, second post: MCEBuddy - Solution to Common Issues and Errors
You can however run mcebuddy as a command line engine from the user login from the start menu which gives mcebuddy access to mapped drives, but then it no longer runs in the background and only runs as long as the user is logged in.