Hard to say with any accuracy since we don't know the draw or duty cycle of this fan. Fans specs should indicate how much power (watts of amps) is consumed and does it run all the time or only at certain temps which would help determine duty cycle.
Since the fan is more than likely a very small draw, battery will behave about the same as before the install with slightly less performance, overall the change won't be extremely noticeable. Hopefully we are only talking about a few days, to expect more from a single battery is asking a lot.