There is very little in the way of bacteria in the water so it will not help a bit. If you were washing filter media or rinsing items that are to go into the tank the advantage of using the used water is not to wash away all the bacteria in the media or kill it with water that is too hot/cold or not dechlorinated (out of the tap). There is no benefit in putting old water in a new tank. The one thing that would help is to put a small piece of the filter media from the old tank to the new filter. It will seed it and actually be the fastest cycle other than to use Bio-spira. You just take like about a third of the pad or such and put in the new filter with the new media pad and let it run. Gravel from the big tank in a cheesecloth bag is also a super good seeding agent. The best locations for bacteria are the filter media and the gravel of a cycled tank.
Welcome to Fishlore.com and I hope I have been of help.
Rose
