it really depends on how the carp takes your bait ... but i find it's more often that they give you a strong tug rather than short small ones initially. Once the carp sense that it's being hooked, it will make a run for it for sure ... i have never had one that just sit there after it gets itself hooked. This all happens within like 5 seconds or so.
you might want to talk to cliff (ccmt) about this. he doesn't like to use bite alarms/indicators as he likes to feel all the action (nibbles, bumps, takes). I use my alarm all the time so all i hear is beeps ... he can give you more insight.