To expand upon what jnorm said, Penny, you've basically got a false dichotomy going and you're also desacralizing matter. God doesn't act spiritually, He came in the flesh, eating, sleeping, dying on a wooden beam, rising in a body. He ministers to us with a book, pen and ink, and people's vocal chords and water and wine and bread (metaphorical or not, makes no difference in this context). Why are the elders commanded to anoint with oil? Why make a big deal about leadership passing through the laying on of hands? There's physical space and action right there, visible things being used as part of our salvation whether we meet in a building with icons and altars and incense or not.
The big problem I have with your view is it leaves no substantial meaning for the meeting together. If Jesus was preaching your view, I don't think He would have said, "Wherever two or three are gathered, there am I in the midst of them," He should have said, "Wherever at least one is gathered in my name..." One might as well just post on a website all there life and call that "Church." Your view doesn't just reject Orthodoxy, it rejects 90% of Protestantism and winds up with Harold Camping and Otis Q. Sellers. The corporate worship and Eucharist basically becomes a nonessential coffee klatsch because you're swapping the Catholicity (wholeness and completeness) of the local Church for the Catholicity of the individual. We're physical beings as well as spiritual and we're saved that way, in our bodies and in a community.
On the other side of the token, to say that the Church is visible is not of course to say she is
only visible. Your point about being able to tell who is and is not in thus misses the point. He who is in the visible Church, might not be in it invisibly as well- he needs both. Just because the question of whether this works the other way around is a contested one does not invalidate the importance of the visible.
And in Orthodoxy, Jesus is
still the visible head of the Church, He's there in the Flesh every Sunday