This question runs the risk of being silly and I think I know the answer, which is "nothing" but I figured I would make extra sure anyway.
I tend to upgrade my servers doing a dist-upgrade and most of the time I ignore the prompt for rebooting (when a kernel gets upgraded). This happens regardless when you have unattended-upgrades on so I don't see this being a problem.
What happens if you never reboot after all these upgrades that prompt you for reboot?
Furthermore, what happens if one of these upgrades is a security upgrade? Does that mean the system is insecure until a reboot is performed?