How to apply updates with VUM to the vCSA host?

This is my first run applying updates to an ESXi 5.0 server and I need some advice, please:

The ESXi host is running the vCenter Server Appliance as a VM.  The Update Manager is running on a separate server altogether.  If the updates are initiated by the vCenter VM, is it possible to update the host the vCSA is running on?  How would you start the updates....  Via the update manager and the vCSA gets stopped/started automatically?

I am also wondering if you recommend being on-site with e the ESXi host during the upgrade.  I assume it's a good idea, but would like some feedback on whether it is always necessary.

Thank You,

~ Michelle