It usually does, assuming you have added sufficient seeded media material to have established a suitably sized quantity of beneficial bacteria to begin with, and you do in fact start out with a very light initial fish load, say just 2 or 3 fish, and add a few more, slowly, every several days apart or so.
I'm not sure of an exact answer but about a year ago I moved twice and had to move the fish. I upgraded the tank size each time as well and added "new" stuff to it, plants, driftwood and gravel as well as taking all of the stuff from the old tank. I also added the filter from the old tank as well as a new filter. I did not loose any fish either time and the tank was stable in about 2 weeks both times. Like I said, I don't know all the forces at work, but it worked well so I am a believe in using established media.
I have taken bits of media from several tanks, combined these bits into a new set up and stocked immediately.
The donor tank can usually spare up to 25% of its filter media, as long as it is well established so there are more bacteria on all the surfaces of the tank as well as in the filter.
If you do not share any media, nor any other source of bacteria, but do the fishless cycle right it takes 3 weeks.
Depending on how much bacteria you add, and what your final stocking level will be the cycle will go a lot faster, up to and including OK to stock right away.
A planted tank will have a fair amount of beneficial bacteria on the leaves and other plant parts, and the plants themselves are part of the bio filter, so a densely planted tank in the hands of an experienced aquarium keeper can be stocked right away, too.
Its always good to have a few sponge filters cycling in well established tanks, then you have an instant filter. Still have to watch your levels for a few days beacuse it is in no mean instant just quicker. You most likely will see a mini cycle as the tank gets going