You can use the USB recovery method to boot to USB. As long as it's bootable and does not require UEFI, it doesn't matter what OS it is.
Note that your NAS will continue to try to boot from the flash memory (and then pass control to the OS on the drives) even after you install Ubuntu, and that will fail unless you go in and make (usually irreversable) changes to what's in flash and/or change a BIOS setting (if there is one that'll work, I've not looked).
If you Google it, you will find instructions on changing a ReadyNAS Pro to generic Linux/FreeNAS, and the process for handling the flash on your 516 should be similar.
BTW, Debian Jessie, on which the current ReadyNASOS 6 is based, is still in the long-term suport phase. It won't be for much longer, and Netgear has never pre-announced when they will be switching over, but I suspect they are already working on it.
Here is my basic advise: If you need somebody to give you explicit instructions on how to do this, you shouldn't be doing it. Use a cheap PC for this instead and sell the 516 on eBay.
I would not try changing BIOS settings on the RN516. Some changes have led to bricking of NAS units.
Changes to the internal flash should be reversible by doing USB Boot Recovery on OS6 systems (though of course there’s no guarantee). There’s not the EEPROM corruption issue when doing this that is seen on RAIDiator-x86 systems e.g. the Pro.
