Should see results immediately uppon addition if the media survived transport. Whether the tank will be immediately cycled will depend on many variables, as Waterdrop states. To deturmin the likelyhood of if the tank is immediately cycled, we need to look at the following;
Stocking of mature tank in inches
How many filters run on the mature tank
How much marture media you have as a proportion of the media left in the mature tank
The size of the new tank.
In theory, if you have 20 inches of fish in the mature system, and you take 1/4 of it's established media, you will introduce sufficient bacteria to suport 5 inches of fish, or suffice to instantly cycle a tank of 5gal or less. You will get some die-off in transit, but an established filter colonie will quickly multiply to replace it's losses.
HTH
Rabbut