Can you get a student discount on a refurbished iMac?

No they don't. But check voucher code sites to see if you can get an online discount before you buy.

I'm not to sure but I know that Student Price card (SPC) does not give you a discount. According to student-discount-card.co.uk in the UK you get 10% off with the NUS Extra card.

they dont do it online but they do it instore

ecampuscash.com offers thousands of discounts from college and universities throughout the country. These college coupons may be printed or accessed via your mobile phone.

Yes, when purchusing from Apple show them your student ID. Usually 10% off or a free gift if they are having a promotion.