Dechlorinator works instantly as long as there is a bit of circulation in the bucket or tank, it doesn't take much.
The amount of chlorine added to tap water is enough to assure that any bacteria in the distribution system do not end up in the water at the end of the system, this being your faucet. These are a very small percentage per volume compared to an aquarium when you take a mature biological filtration system into account. This is the reason additional chlorine is added to swimming pools, if the amount of chlorine in tap water were able to neutralize an unlimited amount of bacteria this would not be needed. It would also mean you could use tap water to disinfect anything, making household disinfectants unnecessary.
This is not the case with tap water, if it were it would make it undrinkable. This is one of the reasons many people get away with doing water changes without treating the water; there is far more bacteria in the biological filter than the disinfectants in the replacement water are capable of neutralizing. It may knock back the bacteria an insignificant amount in a mature filter, in a newly cycled tank this could be quite a bit more significant.
As far as water changes without using dechlorinator, there is a very good topic on the subject
here.
Most of my tanks are drilled with overflows for water changes, just hang a hose & add water, 5gpm. I add Prime afterward more for the removal of any metals, per that topic I've found that with smaller water changes and a mature filter it isn't really needed.