Typically no since the firmware is stored on the hard drive.
One option is to remove the hard drive from the My Cloud enclosure and connect it to a PC (using either a spare SATA port on the PC or a SATA to USB adapter) and see if that PC can read the hard drive. Note that the My Cloud hard drive is formatted for Linux so if you are using Windows you will need to use a third party software/driver to read the Linux partitions.
