Oh, no, that's not how pinch hitting works! At least, not in any of the comms I've pinch hit for. Basically you sign up as a pinch hitter, and then if/when the need arises, either the mods email all the pinch hitters and say 'first one to claim gets it!' (Yuletide does this) or they shop it around to people on the pinch hit list until they get a nibble. You're not obligated to write, ever, on the pinch hit list - you just make yourself available if something catches your eye. At least, that's been my experience every time so far.

ETA: Oh, and if it's just a simple 'I don't have time' when the pinch hit is available, that's fine too - you're really not obligated to write when you sign up to pinch hit, not at all.