I don't think it's a good idea to form subgroups and societies within the Church. I even have a problem with the existence of the Archons as a subgroup of the Church. The double danger I espy is that the "group" or "society" becomes seen as a "sub-Church" (which is a problem in itself ecclesiastically), and that this "sub-Church" comes to be seen as the embodiment of a particular virtue which the rest of the Church need not aspire to themselves. One of the big problems I have with some Greek Orthodox Parishes here in Australia is that their "Philoptochos" Societies are only open to women, modelled after the US practice. It's as though men are not required to be directly charitable themselves, or provide support to the poor themselves. The only contribution the men seem to make is to turn the souvlaki at the annual Philoptochos fundraiser (because, as we all know, women are incapable of cooking on a BBQ ). Perhaps if the men in the Parish were made to visit the sick or homebound once in a while, or do some repairs a widow's house, or put some care packages together to send to victims of disasters or wars, they might just have the chance to put Orthodoxy into practice.
Ideally, all Christians are commanded to feed the poor, visit widows and the sick, etc... Some parishes are better able to handle this (esp the larger one's with more tithing), while others are not. Like Thomas mentioned with his parish, my own parish does very little of this type of work (there are no social programs whatsoever to my knowledge). And, again, for the sake of clarity, I don't think it's a good idea for any religious organization to be 'secret' unless member's safety becomes an issue. And as far as the organization becoming a sub-church, I agree that this presents a problem. Yet this can be addressed by submitting to one's priest and bishop. If they were to say 'disband the group', it should be disbanded.
In defence of this type of group, organization, or society, I see that it has the potential to stir up complacency and give a sense of pride when it attains it's goals. They also have the ability to reach beyond it's home parish and help bring about a little more unity (such as when members of separate jurisdictions join).
I could be wrong here, and there is certainly a degree of concern when forming an organization, but if the priest and bishop give the blessing then why not?