They're good for that first solo, yes. The other instructor has primary responsibility, although you're not going to let them fly if they're obviously tired or drunk or something. But the student is going to need more solo endorsements after that and those are all on you. Specifically they're going to need *at least* A.9, A.10 and almost definitely A.7 at some point (these are all from AC 61-65H), and the only one of those that isn't on you to provide the training for is A.10.

But the answer to your specific question is yes, they're good to go up and do pattern work or practice steep turns or whatever within 25 miles of the airport. But that's it.