If it can't get an encrypted timestamp signed by a particular private key then it knows it doesn't know what time it is

Probably it's like the Nintendo 3DS, the user facing clock is just an offset to the official internal timer, so when the user changes time, it's just an aesthetic change and has no effect to time/date game unlock mechanics (mostly lPokemon games). When CMOS dies, internal clock resets to 1970, a clearly invalid date where all the signing certificates are invalid, and the user can't set internal clock without hacking the console