I have a HP ProLiant server and I'm planning to expand the RAID capacity. I never upgrade the firmware of anything.
Can I add the new disks without the firmwares upgrade or it is absolutely necessary (and why in this case)?
Necessary - no, advisable - yes.
It's because the updates are generally there to fix bugs, one bug that might be fixed might screw you over doing what you want to do - thus by upgrading you're reducing the risk of the work you're doing somewhat.
For your specific question, you can add disks without firmware updates. If the RAID controller thinks the disk firmware should ABSOLUTELY be upgraded, it will actually ask and give a
I recommend running HP firmware updates often... either every 6 months on current hardware or at least yearly on older gear.
One of the unique things about HP ProLiant servers is that firmware not only fixes bugs, but often brings new functionality to the system components. That's not the case with other vendors.
Finally, many compatibility and stability issues are resolved through firmware. It's one of the first troubleshooting steps I advise users here. See: I'm tired of answering questions with: "Upgrade the firmware" or "Run updates"
HP have made the process of firmware updates a bit safer by offering a full bootable DVD image through the HP Service Pack for ProLiant. Download it and boot your system. It takes care of the rest. Failures during updates are extremely rare.