Yes and no. Sins of heresy cannot just be confessed and forgotten. There is a requirement for public abjuration of the error, since heresy is a public sin. Also, in "normal" times, priests would have to get the permission of the Bishop before absolving heretics of sin, to make sure the heretic fulfilled all the requirements to be one of the faithful again.
But, overall, I agree with your general principle that a heretic is still part of the Church, just an excommunicated member. This is different from a pagan or some unbaptized protestant, who has never been a member at all.
This is not true Pax, Canon Law states a public abjuration is required only for adult converts prior to baptism, or if the pope or bishop requires it, or if the confessor requires it, or if public abjuration is officially attached to that censure, other than that the norm is no public abjuration. I posted the applicable Canon Law a few years ago, it's out there if someone wants to find it.
Remember, there are reasons for those provisions in this law. I do not know but perhaps one reason for this is likely that a blanket rule of public abjuration in all cases across the board might have the potential of doing more harm than good. Another reason is that the lifting of all excommunications is in the traditional formula of absolution that the priest already says in confession. The priest through the Church first removes the censure, then forgives the sin.