I think it would be pretty cool, something that you don't see very much of.
1. Should it be done before "truing and rebarrelling"?
2. Would it strengthen or weaken the action?
Case hardening is a broad term. http://en.wikipedia.org/wiki/Case_hardening
I assume you are looking for the wonderful blue colors that we all see in Trunbull pistols and rifles.
All the carburizing methods mentioned in the wiki article, increase the hardness of the surface, but the layer is only thousandth’s of an inch thick.
I would think the best way to go is to have your receiver checked out before case hardening. If the receiver seats are very uneven it would make sense to have them trued before case hardening, then have them checked afterwards. I have always been hesitant to have any material removed from bolt lugs and receiver seats as truing removes the wear resistant layer. If you get 75% lug contact, that is good enough and the surfaces will shoot in to a higher contact level. The only truing I demand on my rifles is receiver face truing.
Case depth is in terms of thousandth’s of an inch. It is a wear resistant layer, while the case does add something to the strength of the piece, it does not change the yield of plain carbon steel to that of an alloy steel. If you want strength you go with alloy steeled receivers.