Inspect firmware update using RACADM command-line utility which provides a scriptable interface for Remote Access Controller.
Inspect job queue for firmware update tasks.
$ sudo racadm jobqueue view | \ awk -v FS="\n" -v RS="----------------------------------------------------------" '$0~/Firmware Update/ {print $0}'
[Job ID=JID_231925652951] Job Name=Firmware Update: SAS RAID Status=Scheduled Start Time=[Next Reboot] Expiration Time=[Not Applicable] Message=[JCP001: Task successfully scheduled.] Percent Complete=[0]
Simplify it a bit to detect if reboot is required.
$ sudo racadm jobqueue view | \ awk -v FS="\n" -v RS="----------------------------------------------------------" '$0~/Firmware Update/ {print $5}'
Start Time=[Next Reboot]