Well, a 166.0324 would belong to a service case, but I don’t think it is technically a service caseback for an old case. Although, it should work. As far as I know, Omega stocks 166.0024 and 165.0024 marked service casebacks for the vintage cases.
Either way I don’t think the caseback is right for a no date watch. I think
@Archer posted some details a while back about there not being a 165.0324 case sold by Omega. That’s why there are a ton of no date WatchCo type builds with 166.0324 casebacks.
Are you sure you don’t have a complete service case for a Seamaster 300 date with the internals from a no date?
Do you have photos?