He will be given a chance. He'll probably be invited to several rookie camps or workouts along with other undrafted players.
I'm a little surprised that Ivy basketball isn't better. Sure, there are no athletic scholarships, but if a kid is poor and gets accepted, he gets a full scholarship whether he's an athlete or not. And if a kid is good enough to make it academically at Stanford or Duke, he or she can probably handle one of the Ivies.
Certainly the Ivy league competes on a national level in sports other than football and basketball (e.g hockey, baseball, lacrosse, soccer, swimming, skiing, tennis). I understand why Ivy league football is different (Div. 1AA and all of that), but I do not understand why Ivy basketball does not attract better players.