According to the Parallels Desktop for Mac licensing policy the answer is no.
In accordance with the End User License Agreement terms and conditions, a Parallels Desktop for Mac retail license can only be used for activation of Parallels Desktop for Mac on a single Mac machine.
Note: In order to use Parallels Desktop for Mac on several Mac machines, you need to purchase the corresponding number of licenses.
You'll probably get a more definitive answer if you ask on Parallels support page. In general, though, if you install an application on more than one system, you have to pay for it again. Note that this is not true of all applications, so you should read the licensing agreement that came with Parallels and / or ask them.
Best of luck.