I am reading two different issues. First is a student who might be suitable for the yeshiva’s incoming class but a shidduch between school and potential student has not yet taken place. There would be nothing wrong with asking current talmidim who the school might seek out for mutual benefit with no obligation to either side until formal application process takes place. That is how universities assemble their varsity athletic teams or encourage national merit scholars to attend.
The more questionable process involves assessment of a potential student who has already expressed interest which generally includes providing a cadre of personal references but the school then seeks additional references surreptitiously and without the candidate’s consent, or even knowledge. Dina d’malchut dina. There are states that have laws that specifically require disclosure of referee comments to the candidate unless specifically waived. The yeshiva seems to be bypassing that legal protection in what it is doing. The potentially unwelcome assessments of the student have no particular accountibility for what they say nor does the school incur a responsibility for verification. Probably not a good practice. I’ll let others assess whether it is appropriate to halacha.