ORD-NRT-BKK should be fine, both are Star Alliance, so NH should be able to book you through. I've booked through UA/NH no problem. The way back could be problematic if you have checked bags. You can't check bags through Zipair to NH and Zipair only interlines with itself, and only on very specific flights listed on their website (SIN-NRT-LAX for example).

That said, assuming Japan doesn't open by August, if you are carryon only, you should be able to check in for your NH flight at the transfer desk at NRT (keep in mind no overnight layovers at NRT), or you could attempt to check in at the NH desk at BKK (I've done this in the US, not sure if it'll work at BKK) if they are open when you're there and just get that piece out of the way early and get your boarding pass.

Someone did raise a question in this thread a few weeks back about whether Zipair arrivals in NRT will allow you to proceed to the transfer area, but from my memory, all arrival flights end up being ushered by the transfer counters, regardless of airline, before immigration.