Dell’s website seems to suggest it can be done from the boot menu independently of an operating system:
Updating the BIOS from BIOS Boot Menu (independent of operating system)
Copy the downloaded file to a USB drive. You do not need a bootable USB drive.
Insert the USB drive into any USB port.
Power on the system.
At the DELL logo screen, press F12 to access the one-time boot menu.
Select BIOS Flash Update in the Other Options section.
Click the … button to browse the USB drive to locate the downloaded file.
Select the file and click OK.
Verify the existing system BIOS information and the BIOS update information.
Click Begin Flash Update.
Review the Warning message and click Yes to proceed with the update. The system restarts and displays a Flash Progress bar at the Dell logo screen. The system restarts again when the Flash update is complete.