I know in certain cases, Horowitz transcriptions, Art Tatum's jazz, etc. improvisations have been dictated by study of the recordings. I saw in a store a written out improvisation of one, Charles Ives, which I believe also was written down by someone other than Ives...must have been taped. However I have from experience, improvised onto the page, this without an instrument, and I'm sure others have done so. Improvisation is the bases of so much inspiration, I can image a single idea springing forth like a seed, which grows into a tree in the compositional process. I don't know if that answers anything.