AppHappy
does receiving your invitation to interview earlier or later mean your chances are better/worse of ultimately being accepted?
No. I wouldn't worry about that. I've spoken to a few alums and applicants from previous rounds who confirm that the dates interviews are granted are pretty random and depend on a number of different factors (region, co-ordinator, time adcom reps reviewing applications take to conduct reviews etc.)
If you get an interview, you're on the same level as everyone else -but for all the distinguishing elements of your application of course.