Some CA's report all of their accounts every month; some CAs only report in batches as they receive the files and then never report on those accounts again. If they are updating their tradelines every month, then the next time they report they should show a zero-balance - which will usually be within 15-45 days.
If they only reported your account once when they first got the file, then it will take a manual update for them to report zero-balance. Theoretically, they should manually update the account status when it is paid; but they aren't violating FCRA by not updating until you actually dispute it. So they usually don't take the time to update unless you beef about it.
Once you do pay it off and then dispute it, they will be obligated to report that it is a paid collection. They don't necessarily have to remove it when you dispute, but they would have to show a zero-balance/paid status. If you want it completely removed from your credit, you usually have to negotiate that up front and make it a part of the payoff.
You would want, in writing from their company, that upon receipt of your payment, they agree to remove the account from your credit bureaus. Don't take their word over the phone, because they will say anything to get you to pay, and then later you don't have proof of it.