Hi Sandy,
I can at least confirm that the firmware update will require a restart of the system, most of the ones I've dealt with from the OEM's pretty much do this automatically without the need for user intervention but does caution that system will restart once firmware has been applied.
We do supply the OEM's, ie., HP, Lenovo, Dell, etc...with the bits for them to package the firmware for their products, so ultimately the OEM is the only one that can inform you of "options" that they may have baked into their firmware updates.
Sounds like you have the right approach of deployment method and only hiccup is a "silent/no intervention" install of the firmware, which is what would have to be supplied by HP.
Most of our large customers using SCCM are creating a task sequence that pushes the firmware out and restarts the system. Possibly a way around interrupting the end user would be to schedule the task after hours with SCCM to apply the firmware update.
Hope this helps,
Regards,
Michael