Rainey wrote books that sound very much like what Stephen describes above. I looked long and hard at the Rainey books, thinking to use them. I was all ready to print out the pdf of his Inductive approach to John.* But then I discovered more efficient (εδοκησεν μοι) methods of treating Greek as real communication (TPR, TPRS, WAYK).
Rainey wrote two for Greek. One on the Anabasis. One on St. John. He also has a book using that style with Genesis as well as a Hebrew syntax and reference grammar. I don't have the links handy. All are downloadable pdf files. Search for Rainey-Greek-Hebrew-Inductive.
I think, that an approach like this would work, if beginnings were made with a communicative approach to embed the meaning of the basic structures of the language and also confirm in students minds that this is truly language/communication. To me, the key difference between grammar/translation and a communicative approach is not staying in the target language or teaching without reference to grammar. The key is to approach Greek as communication, not code. If someone tells me one line of a text from Caesar's Gallic Wars, tells me all sorts of grammar about it, explains it fully and so forth, that doesn't mean I am NOT going to take it as communication. But somewhere along the line, my brain needs to hear that line as a "voice." TPRS, might do the trick here. This TPRS technique of reading a line from a story and hammering it with 3-6 questions (in Greek) is a great way to trick the brain into feeling that these are living words that I need to understand. Done this way, a approach like this might well work. But I can't see it as an introduction to Greek (despite Rainey's title).*
* "An Introductory New Testament Greek Method together with A Manual Containing Text and Vocabulary of Gospel of John and Lists of Words and The Elements of New Testament Greek Grammar" by William Rainey Harper and Revere Franklin Weidener. 1889
Paul D. Nitz - Lilongwe Malawi