I've thought of doing that and think that it's an excellent idea.
After all, the lining is exposed to wear too, and to the potentially-degrading effects of perspiration. I guess we don't do this much because we don't want to get conditioner on our socks, but I think that if you really rubbed it in and then removed all the excess carefully, by the time you wore the shoes again, very little, if any, residue would end up on the socks. I think I'll start doing this too. And Crema Alpina is a really great conditioner. I've used it for some time, but now the stuff I'm getting from Franco's is called Crema Nubiana--which Franco's say is the same thing renamed.