Although elite colleges are indeed swamped with Asian applicants, admission officials often still have a soft spot for “mutts.” Students who hail from more than one ethnic or racial background can sometimes be good “bridge builders” in a college community.
Because your son is only one-quarter Pakistani, his heritage may not affect his outcomes at all. Certainly at Stanford, where applicants hail from every conceivable background … and from many combinations thereof, it won’t make a ripple. But Vanderbilt and ND aren’t quite as diverse. So it can’t hurt for your son to include a mention of his Pakistani roots and it might even help at least a little.
Frankly, “The Dean” longs for the day when questions like this aren’t asked and when race and ethnic “strategizing” isn’t part of the admissions process. But, for now, it IS, so you might as well try to use it to your son’s advantage.