In my experiences, using
Debian GNU/Linux is the best for administering remotely, due to the amazing apt tool. I run a server and I administer it completly remotely using ssh. You can upgrade your linux kernel remotely, it's not recommended, but it is quite possible. After you compile your kernel, and install it in /boot , you can edit your bootloader to accept it, and double, triple and quadruple check to make sure everything is just right, and then reboot. The last thing you need is a kernel panic on a remote machine.
Like i said, it's not recommended, but there is no reason why can't do it if you want.