Yes. The owner of any prior version of Elements is eligible to purchase the program for a discounted price. The two programs are independent and both can exist on your machine without interfering with each other.
There is no upgrade. Obtaining the most recent version of the software requires a purchase. If you registered the program with Adobe subsequent to purchase, they will offer a discount to you as a repeat customer. Be aware that frequently you can beat this price by shopping around at Amazon or one of the big box stores.