yes, it could infect the MBR on the hard drive which is not wiped in a format. not sure how advanced such a virus is capable of being but I imagine it could be advanced enough to enable something on a fresh windows install to autoload a more complex virus.
Technically I imagine you could infect the "bios" as well, though resetting the bios would likely clear that unless the attacker had physical access to the machine.
Don't think a virus would survive anywhere but the HDD/SSD or BIOS due to everything else being stored on volatile memory. feasible if any hardware you have that can be flashed could be loaded with a virus but that'd be a really targeted type of virus as it'd only work on that specific model of hardware.