I'm assuming no.
The Battle Mansion is like the Battle Facility. It won't record Pokemon you've seen from there. So the short answer: No.
No they don't. It's like Black Tower from black 2,the Pokemon you see there won't be registered.
Source: Experience. I hadn't seen a Mightyena in X and when I battled it in Battle Maison,it wasn't registered.
Hope I helped!