Let's start with their definition of the "organic church":
An organic church is a living, breathing, dynamic, mutually participatory, every-member functioning, Christ-centered, communal expression of the body of Christ.
Sounds a lot like the Orthodox Church to me, lol.
Of course, Viola and Barna are setting up a false dichotomy by separating the "institutional church" from the "organic church". The institutional structure of the Church is itself part of the Church's organic nature, just as the skeleton structures and supports the rest of the body.
But what is the origin of the organic life of the Church?
The Lord Himself gives us the answer:
John 6:53-57 (KJV)
Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you.  Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day.  For my flesh is meat indeed, and my blood is drink indeed.  He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him.  As the living Father hath sent me, and I live by the Father: so he that eateth me, even he shall live by me.
The source of the "organic" life of the Church is Christ, the Incarnate God, who has given us His Body and Blood "for the life of the world". Compare the passage above (especially verse 57) with Jesus' words spoken, not insignificantly, at the Last Supper
John 14:20,15:4-5,8-9 (KJV)
At that day ye shall know that I am in my Father, and ye in me, and I in you....  Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.  I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing....  Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples.  As the Father hath loved me, so have I loved you: continue ye in my love.
We must abide in Christ just as He abides in the Father. Then we will be like branches which abide in the vine and bear much fruit. 14:20 and 15:9 make it pretty clear, in my opinion, that the two passages I've given (the Bread of Life discourse and the Last Supper discourse) are about the same thing, namely, the Eucharist. The Eucharist, the Body and Blood of the God-Man Jesus Christ, is the source of the Theanthropic Life of the Church:
1 Corinthians 10:16-17 (KJV)
The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?  For we being many are one bread, and one body: for we are all partakers of that one bread.
How are the many disparate members of the Church brought together to form one "living, breathing, dynamic, mutually participatory, every-member functioning, Christ-centered, communal expression of the body of Christ"? Through partaking of the One Body of Christ, the Church itself becomes that One Body.
John 17:21 (KJV)
That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me.
Considering that Viola and Barna don't really believe in the Real Presence of Christ in the Eucharist, how do they understand the organic life and unity of the Church?