It's certainly possible to automate this process with PowerCLI. The difficult thing is going to be getting the list of patches required from VUM to a script. Here is how I would do it:
1) Get the list of patches from VUM and then get the d/l links from the patch portal.
2) D/L the patches to a local directory and then copy them to the datastore.
3) Execute the patch installation commands with get-esxcli commands.
4) Shutdown the vCenter server and reboot the host.
Obviously there are a lot more steps in there, but it's a good starting place. If I ever get some free time, I might look at creating this script... 
EDIT:
Here is a blog post that goes over all the options for CLI based host updating.
Message was edited by: McKenning to add a link to a vmware blog post.