Yes. If you need to move your license key from one site to another then simply deactivate your license key on the old site and then you’ll be able to activate it on the new site. If you have a multi-site license (such as the Business license) then deactivating your license key on a site frees up a “slot” on your license so that you’ll be able to activate another site. You may find this FAQ on site management to be helpful as well.
You can also transfer a purchase for a plugin/license key from one Smash Balloon user account to another Smash Balloon user account if necessary. Please see this FAQ here on how to accomplish that and what it entails.