That's basically a chapter's choice.
Some chapters have rules on who can wear letters, other's don't. The only thing restricted in the Black Book (Int. bylaws) is that non initiated people can't wear the crest.
I'd say for priviledges, it'd be whatever the chapter wants to do.
If you really want to find the end all answer, get your hands on that chapter's bylaws, and see if there's anything about it in there (if they keep it up to date)
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