

No, that wouldn’t make much difference. I don’t think I’ve seen a real world attack via SMS that even bothered to “forge” the from-field. People are used to getting texts from unknown numbers.
And how would you possibly implement this supposed “caller-id” for a field that doesn’t even have to be set to a number?
That’s hyperbole. Such a system can be “hacked” by simply plugging in a usb-stick and booting from that instead, or dozens of other ways.
The only reason to use GRUB authentication I can think of would be in something like a kiosk.