You should still reboot your Linux server regularly. While the updates can run in place, running processes will not pick up the changes until restarted. And when you update the kernel you also need to reboot the system to pick it up. While there are distributions out there that have systems in place to auto restart affected services and can upgrade kernels in place (e.g. Ubuntu with the right licence), it is still recommended to reboot every now and then. My server is set up to reboot once a month and after every kernel update.