I didn't see a need for using carb cleaner or anything on them once I had finished. These carbs have been sitting outside for years, so most of any gas that was on them would have been absorbed and blown away in the dirt/dust. There were very few spots of noticeable grease, and those all cleaned up with very little work from the soda blast.
The soda didn't really polish the surface of the carbs. You could still see the original casting surface once they were cleaned up. And it didn't take much to paint them -- just a light spray to stick the surface, then several passes to get an even coverage. There's been no sign of wrinkling from missed oil residue, and I didn't have any problems with paint trying to flake off when I peeled the tape, so it seems like it stuck well.
What worried me most was that I didn't consider a powder residue being left by the soda, however I know most times spray paint is pretty good about encasing and soaking through any bits of dirt left on the surface, so hopefully it also soaked through the soda and this won't actually be a problem. At this point the paint should be pretty solid, so maybe I'll just spray them down with the water hose and see if anything knocks loose.