Yes, those wheels would use the same 3.25" bolt circle sprocket that your series II wheels used. Does not look like roadrunner used a brake on it though, It looks like they used a band brake off the jackshaft in this pic......I'll know better soon as I have to pic this bike up from another member to get cleaned up, sorted out and sold off:
General Appliance did in fact briefly use those wheels too, The one I had used a pretty wide spacer and flat bolt on sprocket, but was a swingarm model (dunno what a non suspension frame has for room). what brake would depend on model I believe, they liked to use the band off the jackshaft or a larger band brake on the wheel for the most part.
fitting a drum brake will require mounting stop lug onto the frame most likely. For instance this trail blazer below that I had bought to part out a few years ago had Azusa tri stars on it, with the Azusa flat drum brake. Not the best photo's but you can see they welded a 5/16" round spacer/bushing to the frame so the brake stop ear had something to bolt to (right side bottom frame bend). It worked pretty good on the one ride I took it one before it went under the knife :grind: