No, a Mobile Link account and network connection are not required for a home standby generator to operate. Automatic operation for a home standby generator is configured from the generator control panel. Note that there are many benefits to using Mobile Link, and a basic plan is offered.
Mobile Link Benefits
What is Generator Registration?
Generator registration is the process that you or your Dealer/Installer goes through to put your generator into automatic mode. This also starts your generator's warranty. This is most likely handled at the installation of your generator: How Do I Activate My Home Standby Generator?