Abba_S: The problem with the approach you describe is that
1) once they start dating they may become infatuated or fall for each other – and then it may turn out upon further research that the match is inappropriate, and
2) if the girl says yes and then finds out within a few days, prior to the first date, that it is inappropriate, can she then change the yes to a no? Going out because she already said yes, when they know it is going to be a no thereafter, is even worse. It is a) wronging the boy and b) you might encounter my Point 1 where they both want to continue and it will be difficult to break it off, even though it is an inappropriate match.