Is your house system a stereo system or mono? In other words, do your odd groups feed a left cluster of speakers and your even groups feed a right cluster of speakers? If so, then by panning the background vocals you just removed them (somewhat) from the left speaker cluster, which is probably not what you want.
If instead all of your groups are getting summed and are feeding mono speakers, then you could take your idea even further and hard-pan the lead and background vocals to different groups to give you even more independent control. This is commonly done (not just with vocals) so that your 8-group board can really be used to create 8 independent groups (instead of 4 pairs).