It could be something worth studying but I think you'd have to work very hard to tease out all the variables.
The variable I'd add in there is the lifestyle of your average post secondary student. Even if you're not a partier (I wasn't) the student life can become pretty unhealthy rather quickly.
If you're spending most of your time doing readings, labs and assignments, you're probably spending a lot of your time being physically sedentary. Yes, sometimes I got reading done at the gym but that only worked if I didn't have to take notes for the reading.
You're also less likely to have time to properly grocery shop and cook healthy meals, and depending on your living situation, you may not even have resources like a fridge and stove. I joke that I got through grad school on chocolate and adrenaline - and I am not really exaggerating by that much.
One of the elements of post secondary education is that you're supposed to focus on matters of the mind - not the body.
I'm not sure if controlling for that would work for or against the potential thesis but I do know that I was obese when I graduated and I've seen a few others on this forum whose starting photo is a graduation photo.
I suppose another factor to take into account is whether one's ability to complete higher education is necessarily a measure of one's intelligence.
Balance in all things.