E.g. there are open positions for just-hired faculty that one can see at "rumor mill" places like http://www.astrobetter.com/wiki/tiki-in ... ulty-Staff
, and we might learn more in the coming months. It's possible that someone might get an appointment by autumn, in which case they might be able to take a new grad student right away (or soon). Does that ever happen?
And could this also potentially extend to people who got in (and are visiting) as well?
Please don't. First, rumor mills are, by definition, rumor mills. They are sometimes wrong. Second, newly-hired faculty are very wary about "making waves", and they certainly aren't going to do anything that would affect the work of the admissions committee. Third, there are likely first or second year students already there who might want to work for the new person, and they would have higher priority---the newly-hired faculty member would likely want to wait to assess the situation.
If you've already been admitted and are interested in working for an allegedly newly-hired person, then it is perfectly ok to contact someone else
in the department (preferably in the same subject area) and mention your interest in working with the newly-hired person. That person will best be able to judge the situation and may or may not contact the newly-hired person about it.