depends a bit on fuse/breaker type and typical loads. If you look at the charts, you'll see that traditional thermal breaker will take 10+ minutes (I vaguely rembmer it being around an hour) to trip at their rated current. It's a logrithmic scale, with higher currents tripping substantially faster. I suspect slow blow fuses are similar, but haven't really looked at the specs.
So, if a drained battery draws 40+ amps for a minute or two, it likely wouldn't be a problem. Just look at the charts for the fuse type.
Larry