Probably? He definitely wants them to be connected to each other by more than blood–and he does teach all of them Grand Fireball when they turn seven, probably, but given that actual clan status (as the Nara go, anyway) involve things like clan tax and land/etc and there’s only one adult and maybe six kids at most they’re not really capable of being a clan yet. Eventually? But not yet.
Especially since they all live in different households raised by different people. Not sure if Sasuke arranges meetings with the kids. If so, it’s definitely infrequent.
Sakako is probably the oldest (maaaybe Sarada is older?) and so she and Sasuke get to make up the new Uchiha clan traditions. More like coming of age sort of things–seventh birthday, becoming a genin, etc etc. Maybe they get to learn Sasuke’s Fire variant of the chidori at age twelve?
Since the Uchiha matriarch-to-be is half Nara, it’s very possible that the fledgling Uchiha clan “officially” becomes an ally of the Akimichi-Nara-Yamanaka alliance and so there’s an exchange of benefits there. The new Uchiha clan get their ears pierced at becoming chuunin (maybe genin, too, like the A-N-Y clans, but definitely chuunin).