As far as I can tell, no. You could try keeping an eye on the following page: http://tardis.wikia.com/wiki/Torchwood_Institute_-_List_of_Appearances. Please note that it seems to be slightly outdated (Torchwood Series 4 is represented by only one episode) but it's probably as good a place to look as any.
Note: When the (10th) Doctor encountered the Torchwood Institute in "Army of Ghosts"/"Doomsday", he'd apparently never met with it before. If any spinoff production did have an earlier incarnation encountering it, there's a good chance the story would be written in such a way that the Doctor didn't know it was Torchwood he was dealing with.
Keep in mind that the 10th Doctor indirectly created Torchwood in "Tooth and Claw". If this was a case of changing history, rather than fulfilling it, Torchwood didn't exist earlier in his timeline. (But of course we don't know which of the two cases it actually was.) In the novels and audios, there were a large number of similar organizations, and in one novel (I forget which, but I think one of Keith Topping's), the Doctor explicitly said that there were undoubtedly more such organizations out there that neither he nor UNIT had ever heard of.
According to the old official website, Torchwood had files on at least the 9th Doctor, and possibly earlier incarnations, even if he never met them.