Hi bleuze,
I don't know if this will be the first time you perform an update? But if so, first of all don't worry about the process.
We have over 500 ESXi Hosts worldwide with something over 25'000 vGuests and I never ever took a backup of a Host before installing an Update.
The only think you have to know is this:
Get your configuration written somewhere in your documentation:
IP Address of the ESXi Host, Subnet, Gateway, which Adapter you are using.
This are essential things that each IT professional should keep recorded at all times, we do have Installation Qualification Documents where we keep track of each ESXi Host and how it's configured.
Now, when you use VUM (vSphere Update Manager) you are creating Baselines or using the ones given by VMWare as a default.
When you hit the stage button it will trigger your Host to install the Updates, it will then reboot automaticlly and it will come up alone.
After about 10 to 30 Minutes your system will be up and running again.
IF, and that never happend to me since I'm using ESXi 4.1 the Host would not reboot and stuck or be damaged.
Just reinstall the ESXi version you had. (Make sure that the vGuest Configuration is not running on the System Partition where the ESXi is installed) What I hope is not the case, as this is NOT at all to be done! So if you reinstall then ESXi you can then just re-add all the IP Information, add it back to the vCenter, configure the Network and then just add the vGuests by Browsing the Datastores and adding the VMX files of the vGuests back to the inventory.
But as I sayed I bet you 1 BitCoin that this will never happen! (It never happend to me and other collegues that I know of)
Best of luck!
Marco