I'm not sure if this is precisely what you are looking for, but your question immediately reminded me of Augustine's City of God:
Chapter 35.—Of the Sons of the Church Who are Hidden Among the Wicked, and of False Christians Within the Church.
Let these and similar answers (if any fuller and fitter answers can be found) be given to their enemies by the redeemed family of the Lord Christ, and by the pilgrim city of King Christ. But let this city bear in mind, that among her enemies lie hid those who are destined to be fellow-citizens, that she may not think it a fruitless labor to bear what they inflict as enemies until they become confessors of the faith. So, too, as long as she is a stranger in the world, the city of God has in her communion, and bound to her by the sacraments, some who shall not eternally dwell in the lot of the saints. Of these, some are not now recognized; others declare themselves, and do not hesitate to make common cause with our enemies in murmuring against God, whose sacramental badge they wear. These men you may to-day see thronging the churches with us, to-morrow crowding the theatres with the godless. But we have the less reason to despair of the reclamation even of such persons, if among our most declared enemies there are now some, unknown to themselves, who are destined to become our friends. In truth, these two cities are entangled together in this world, and intermixed until the last judgment effects their separation. I now proceed to speak, as God shall help me, of the rise, progress, and end of these two cities; and what I write, I write for the glory of the city of God, that, being placed in comparison with the other, it may shine with a brighter lustre.
I've emphasized several phrases that say:
- Some of the elect are currently enemies of the Church,
- Some within the Church are not among the elect, and
- The Church and the World are currently intermingled.
It's not exactly the case that false Christians are "invisible"—Augustine notes that they may be found in the theaters with the godless. (Augustine had a very low opinion of theaters at that time. We could probably stand to be more critical of our entertainment choices in this day as my grandmother would have been quick to remind me.)