Not necessarily. If it simply sets the random seed once as the program starts, then saving the state of the game, and reloading it repeatedly will give the same result from rand(), because the seed hasn't changed and you are rewinding/repeating time.
If I flip a coin in a deterministic universe, it's still "random" (air flow, force exerted, etc), but if I "rewind time" and play it back, I'd get the same result.
If I flip a coin in a deterministic universe, it's still "random" (air flow, force exerted, etc), but if I "rewind time" and play it back, I'd get the same result.