Are you referring to this sort of prompt, received when opening an older version of the software (if there is a newer version available):

This prompt will appear if the user has the Check For Updates option checked under Global Preferences > Dynamic Content. The option is checked by default in a new FlexSim installation.
It is simple enough to respond with the "no thanks" answer. Or, go ahead and install the latest and greatest version. It would allow you to try out the new features and see what has changed. It will not be a fully licensed version (unless your license server has already been updated, and then you configure the new install to point to your license server), but it also does not change anything about the licensing or about the previous version.
If you choose to "Upgrade Now", then the older FlexSim installation initiates the download, then prompts the user to close FlexSim and install the newer version. Doing so does not uninstall the previous version - it will still be there, and still be licensed, when the user is again ready to open the previous version.
If the person hits "Upgrade Now", but does not have administrative rights on the PC, it will still download the file and try to run the installer. The installation will fail and exit early, however, if the user does not have those admin rights.
Let me know if you have any follow-up questions.