Hi,
If the sites are on the same domain and IP, the update script should allow the license activation on both. If it does not for some reason, then I recommend activating it on the Dev site only, since you are pushing it to the live anyways. License activation is not required for the plugin to work, it is only for the automatic update verification, it does not limit it’s functionality in any way.
If the sites are separate branches, then you can activate on one, and use manual updates on the other.