i3's typically ship with lesser cooling abilities than i5's or i7's - but I don't recall when that started. For some Gens, I believe the stock HS/F was identical.
No harm in trying, but it's going to be far from optimal. You'll know pretty quickly whether it's sufficient - stock coolers are fit for purpose, and no more. So if it's a cooler for a 65W TDP *only*, you'll know once the i7 is stressed.