What you've described is the core of the cyanotype rex and chrysotype rex processes. With cyanotype rex, instead of mixing the ferric ammonium citrate and potassium ferricyanide solutions, the ferric ammonium citrate (or alternately ferric oxalate) are applied to the paper and exposed, producing (they say) a very faint print-out image, which is then developed with a wash of potassium ferricyanide (for cyanotype rex) or gold chloride solution (for chrysotype rex -- the used solution can then be used as a gold toner, they say, which helps ease the price issue a bit compared to $30 per print for the gold).

With cyanotype, you're producing an iron based final image (Prussian blue, ferric ferricyanide IIRC). If you were to wash with gallic acid instead, you'd most likely get a ferric gallate image, with all the permanence of the iron-gall ink (and, as with the other processes, it would be a photographic negative). You likely would get something similar with tannic acid, pyrogallol, etc.; you'd essentially be creating a gallate version of a cyanotype.

I don't recall reading about anyone trying this -- possibly because the two step, sensitize and develop process originating with Herschel was abandoned for the mixed sensitizer, printing-out processes for cyanotype, chrysotype, and kallitype before there were photographic negatives to print, and before anyone tried Herschel's original (much faster) method in camera.