No. Purchasing an upgrade to your product extends your existing license to cover the new version of Adobe software. It does not provide you with two separate licenses for the old version and the new version.
If you purchase a new license, rather than upgrade your old software, you are permitted to transfer your old license—that is, as long as you did not purchase the original license with a volume licensing arrangement.
from here:
https://helpx.adobe.com/x-productkb/policy-pricing/end-user-license-agreements-faq.html