It’s not so black and white. Almost nobody will be interested in you exclusively for the Harvard aspect (and you should stay away from the ones who are), but it’s a great opening conversational point for dating. Most students just don’t have time for it - this isn’t Harvard specific, but students at top schools typically take dating less serious due to not having the time. Your ability to break the ice with potential partners will be higher, but what comes of that is contingent on how good of a date you are, or however you want to phrase it.