You don't need to have Studio One 2 Producer installed on your computer in order to upgrade to Studio One 3 Professional, but it does need to be registered to your My PreSonus account online in order to purchase the upgrade from shop.presonus.com.
Once you upgrade Studio One 2 Producer to Studio One 3 Professional, you won't be able to transfer your copy of Studio One 2 Producer. You can't transfer software that has been upgraded, you can only transfer the license that is the result of the upgraded license (i.e. Studio One 3 Professional, in this scenario.)