My analysis is that this situation can only be good, coz:
1) The person is already at Cornell.
2) She / he took the time to write about you without you even asking.
3) This process (the "unofficial" rec) works great when you are being recommended by alumni or students who would not normally be your 1st or 2nd recommender. Most schools will add this extra recommendation / e-mail to your file and consider it together with the rest of the package when evaluating your app.
I had the chance to ask a Chicago adcom (during an info session) the following question:
lepium: "I have 3 potential recommenders: 2 know me best as they've been past and current bosses. The 3rd person is a GSB alumnus who has worked with me in some projects and knows me quite well, but has arguably a little less knowledge of me. Should I prioritize the alumnus vs. one of the other guys?"
GSBAdcom: "Well, most GSB alumni correspond with me on applicants, so I suggest you get the recos from the 2 former bosses and then the alumnus can write a note directly to me. Such note will then be added to your file".
I'd say depending on your relationship with the person you can choose to call or not to call him or her. I'd probably write a succint thank you note and see what he/she answers.