Can a rogue using a weapon that deals ability damage (such as a Rapier of Puncturing) use it to do a sneak attack that would deal 1d6 CON damage + xd6 sneak attack damage?
Yes. (Not including feats that allow dice of Sneak Attack bonus to count for special effects,) Sneak Attack damage deals hp damage in hp regardless of the attack form with which it is delivered. If you do it in a Str drain attack as a Sneak Attack, you are correct in thinking it does Str drain normally and the Sneak Attack as straight hp damage.