The US does not have a national higher education system. Policies vary by State by institution, and possibly even by field. Moreover, what is appropriate in one field may not be in another. There are likely also different policies in place for the consideration of candidates with baccalaureates only, vs those with masters degrees.
My guess is that the most common system is to have a committee review all candidates to attempt to assure fairness and even treatment. Such committees will have policies set, perhaps, at the department level or, perhaps, at a higher level. In most fields, professors don't sponsor candidates as they do in some other countries.
Such policies might include the opportunity for exceptions in some cases, or at least taking informal advice from outside the committee. But it is also possible that policies are strictly observed - fairness, again.
On the other hand, if a new faculty member expresses an interest in a particular person, especially in a field in which the advisor needs to be chosen at entry, then their views would probably be considered and even have some weight. How much weight is impossible to say.
On the third hand, I think that if the new hire were at an entry level, Assistant Professor with no prior experience, that they won't have any leverage at all, other than a sense on the part of more senior faculty that a collegial atmosphere is good to establish.
Thus, I would expect that at most institutions, the "boost" such an applicant would get would be small and tenuous. But possible.