The idea of the "invisible Church" applies to few and far-in-between apostate or non-Chrstian individuals who were tuched by the Holy Spirit, and is not something the Church would recommend as an alternative to the Eucharist.
The proper terms are Church Militant, Church Suffering and Church Triumphant. Do the Orthodox use those? "Invisible Church" is sometimes used to describe the mystical body of Christ. I don't understand the term very well, except when it simply means "the Church as the spiritual entity rather than the physical building".