Verify OS X Base System
macOS Internet Recovery is a NetBoot-like service. Basically, a bootable image is downloaded via HTTP (from an Apple or an Akamai server) into RAM and your Mac boots to it afterwards.

So yes, you can run First Aid on the OS X Base System volume and it will not erase, restore or alter partition layout because it's not a writable volume.



Since it has to be assumed that the image was verifed already after the download has finished and the boot process was successful, why do you want to verify the OS X Base System again?