Not in this case. Phone number of the device, name and address. Here is a link to the actual form.I work for a carrier other than Sprint, but I stick with Sprint because of the price. I fill out rebate forms for customers all of the time, and on our rebate form it does have a place for the purchase date, as well as name, address, wireless number, IMEI (or ESN, MSID, etc.), as well as needing to check the box next to the phone you purchased, and the check boxes next to what you include in the envelope.
http://shop.sprint.com/assets/pdfs/en/promotions/mir_071010.pdf