I find the idea somewhat disturbing… Of the “flash mob,” not the adoration, that is.
As an Orthodox Christian, I have been taught to cross myself when passing by a Catholic church, so I suppose I would do just that. I really have no idea what “Eucharistic Adoration” involves from a Catholic perspective.
As for sacraments, the position I’ve usually encountered is that of “we know we have them, and that’s all we can really say.” This is emphatically not to state we don’t think others have them. We’re just not too caught up in spelling it all out–it’s out of our hands anyway, is it not?
Please note, as this may explain the position better, that as far as I’m aware Orthodoxy has historically not designating a precise number of sacraments even for itself. Seven has come into popular consciousness, but I seem to recall reading that this stems from RC influence coming into play during later centuries, at least in the Russian Church (via Ukraine and Kyiv-Mohila). We’re okay with the “spirit moving where it will,” so I think that most Orthodox would not in the least be trying to insult anyone by saying we “don’t know.” It’s just the most logical and theologically consistent answer we can give based on our understandings.
That said, as a cradle old calendar Orthodox (not so much into being PC, my section of the Orthodox world), I can tell you that in my own experience, almost everyone I’ve known among the laity growing up has regarded the Catholic Church as a sacramental church in terms of everyday interactions with Catholics. But according due respect is not the same as agreeing on doctrine. And the distinctions are far deeper than just the Papacy and filioque.