So, once again I can't vote ...
Yes, they belong to the N.O. & adhere to the Catholic Church & they do hold office.
I believe that they CAN belong to the NO, adhere to the Catholic Church, and hold office, but most probably do not, since they are manifest heretics.
So, in the case of a non-(pertinacious formal manifest) heretic [agreeing with your definition of those who merely "belong" to it] with valid Holy Orders (at least for some episcopal functions), e.g. as in the Eastern Rites, I believe that can and do hold office, either by the principles of sedeprivationism or else the "color of title" principle that some SVs have cited from theologians, where those in lower office can still receive jurisdiction from even an Antipope due to "color of title".
I believe that few meet these criteria, most notably some Eastern Rite bishops. There are a few Roman Rite ones who are not pertinacious heretics, but they have dubious orders, and therefore can do little more than make appointments and serve as a conduit for the jurisdiction priests require to confect the Sacraments.