That GPU's definitely not gonna be 100% healthy again. Let it dry 100%, wash it using something that doesn't conduct electricity or something that evaporates. Chemicals such as Isopropyl Alcohol (I'm not a chemist, I don't know if I spelled that right but its the stuff in hand sanitizer) will work, as they evaporate away. Clean off any soda goo with it after it dried off, and it will evaporate on its own.
You want to be gentle with this, so I'd use something like a Q-tip or potentially a paper towel, as to not damage the traces.
After this, make sure all of the soda and the alcohol is dried off of the card. Make sure you have removed all of the potential goo from the card, then you can try to power it on.
Soda is also acidic, so before it dries up, clean it lightly with the alcohol ASAP to get rid of the soda.
EDIT: Looking at that picture again, I can say there's about a 30% chance that it will work again, especially if it's already started to fry itself (the white effect on the screen)
Best of luck to you though, I hope you fix your GPU.