Thanks, Michael for the response to my post. I've not been able to get a clear answer from HP on whether a reboot is necessary or not deploying the firmware. I thought there was an outside chance that since HP is utilizing what I thought was an Intel utility (FWUpdLcl.exe) they might shed some light on best practices for deploying AMT Firmware.
I am using SCCM and have identified all our vulnerable HP models and my next step is to deploy the firmware.