The "upgrade" of Premiere Elements is actually a full copy of the program at an upgrade price -- so yes.
But do note that project files created with the PC version can not be opened by the Mac version and vice versa.
Thank you, Steve. I was actually referring to commercial terms. Would Adobe still think I qualify for an upgrade or do they consider this a completely new purchase ?
Just my opinion...
If you go to the Adobe online Buy for the product, the choices under Upgrade "I own: Select a Product.." do not include a Windows or Mac notation. I am assuming that if you can show proof any earlier Windows or Mac version for anything on the list, you would be eligible for the upgrade pricing. But, the ultimate answer needs to come from Adobe. Have you contacted it yet to ask the question via the Chat link on the Buy page?
Though also note that the "upgrade" price Adobe offers isn't always the best price available. Sometimes people go to Amazon and find a new version of the program on sale for less than Adobe's upgrade price! Sometimes. Anyway, it's worth shopping. It's the same program no matter where you get it.