Sigma Nu does not have "Honorary" Initiation. You are either an Initiate... Or you're not. I did however personally oversee the initiation of several alums that were invited back when we got our charter after 2 years of work... (some had to graduate in that period)... I also oversaw (I wrote and corresponded with HQ on the matter) the initiation of our faculty advisor who is an official of the University that was particularly influential in getting our colony started. He was also been indispensible in our progress towards being a chapter.
Sigma Nu does not grant alumni initiations lightly. All of them must be approved by our Executive Director (I think our High Council may have something to do with it as well). Like anyone else they also require the same vote for initiation as any other active.
But as far as inviting our parents back or initiating friends... that doesn't happen except for in EXTREME circumstances where these folks have demonstrated service and committment.
Hope that helps