Does the downgrade patcher on Nexus work with the GOG version? I'm thinking about buying again here if it does.

I seriously doubt that it would, but even if it did, it would downgrade you to the DRM Steam version that would require you to have the game on Steam in order to play it.
So what would be the point?

Thanks for the reply. Think I'll stick to the Steam version for now and maybe get Anniversary here in the next sale for a non-modded playthrough and to have a DRM free Skyrim copy. In addition to your reply, since my post I've read other things in the reviews and forum here to suggest that modding GOG Skyrim will not be a great experience.

As have been said.. only for subsequent releases on Gog. And it's actually quite easy to do it in the game settings. In your game page click on the "settings" icon (the one with sliders) -> Manage Installation -> Configure... -> <here> You will see a list of patches you can run on in the list that appears (but if they change the location after time of writing, you need to find it yourself) In any case. I'm sticking to the Gog version entirely from now on. DRM free, full control, and Gog fixing the game when changes in Windows break things. Something Steam never does. As far as I am concerned, this is now the "official" version to do mods on. And in regards to mods, very few mods doesn't work on the Gog version (for me, I'm not saying yours do). And at time of writing it is only Papyrus that doesn't work for me. I got everything else working (knock on wood) I'm also only using Mod organizer 2, not vortex.