Probably no strong need to upgrade, but there might be reasons it would be beneficial. The BIOS updates can include performance and security fixes from the CPU vendors, for example. Check the description on each BIOS download that's newer than your current one to see what you would get. It's entirely possible that they may have fixed something which would improve performance or stability on newer GPUs, but probably not. The BIOS mostly uses ancient generic VGA stuff during boot, and the clever stuff is all in the OS graphics drivers; that ancient stuff hasn't really changed much in decades, so cards mostly just work as long as the OS can support them (once the OS is running, the BIOS GPU stuff is basically irrelevant).

You are highly unlikely to do any serious harm by just trying the card without updating (taking appropriate care and static electricity precautions when installing). If you encounter any issues, consider the BIOS version in your troubleshooting.

Your motherboard should be dual BIOS (I think, didn't check the spec sheet, most of the premium boards like Crosshair and Maximus series have had that for a long time). It will also probably have the clever BIOS Flashback / Crashfree BIOS feature, which makes it almost impossible to perma-brick it when flashing using normal end user tools; just insert USB stick with appropriate BIOS file into the marked slot, and follow the manual (press the button on the back). Nothing is every 100% risk free, but they have done a lot to make BIOS updates low risk and easy on the premium boards. The current generation of boards can even flash themselves from USB with no CPU or memory installed, if memory serves.