I was once in the office of a Rosh Mosad of a more right wing school when someone was pressuring him to accept a girl and he answered "The kid's mother couldn't even dress normally for an hour at registration to get her kid into school and you think she is a fit for our school?"
So the answer to this questionCan be yes. Ask any of the askanim and they will tell you this.
Call me an OOT naive guy, but seems wrong to me for the "Rosh mosad of a right wing school" to be basing acceptance policy based on how he judged the mother to be dressed. Wrong both intrinsically as an acceptance policy, and wrong because it will be perceived by anyone in the world as inappropriate for a Ben Torah to be the judge of.
Absolute objective benchmarks such as TV or Internet are a much better way to go.