Especially note: "IMPORTANT! If the update requires a reboot, the computer will need to be rebooted for the updated AMP for Endpoints Connector to work properly. "
Regarding AMP running/not running after upgrade. The only exception/improvement is after AMP 6.2.3. For example when upgrading from 6.2.3 to 6.2.9, reboot is needed to activate features of 6.2.9 version, however it is not required for the AMP to work (it will continue to use old drivers from 6.2.3):
Please also note that there is no option to disable popup about reboot. "Ask for reboot" is just another window that gives user possibility to reboot straight after upgrade. Like on the screenshot below (example from upgrade from 6.2.3 to 6.2.9):