I can't answer your question straight, because I've not done that. BUT, I DID add some gravel from an established tank (my goldfish bowl), and a lot of water from an established tank (from the lfs), and it was cycled in a matter of days! If you have a cycled tank, why not use some of the gravel (in a pantyhose, if you want to put it back afterwards) do occasional water changes from the cycled tank, and instead of throwing away the water, add it to the uncycled tank?...If you have a testing kit, test the water daily, and you'll know when you're cycled. I was new to all this a few months ago, and was pleasantly surprised by the short time it took to cycle Just make sure your ammonia and nitrites are zero before you add any fish, and the nitrates as low as you can get them.
Good luck.
2 or 3 weeks should be good. I do this with spare filters and you can see the color change in the sponges of home made filters. After 2 weeks, it's considerably darker, after a month, they match the older ones.
If you're trying to seed your new tank, move the entire filter including the media into the new tank. A very large amount of the bacteria is on the media rather than the filter itself.