It is not the water that contains the bacteria. The best thing to do is add filter media/sponge from the established tank to speed up your cycle. You can also transfer some gravel over. However, the process is a lot slower than with the media/sponge.
No, it's a waste of time. The water doesnt contain bacteria. Even the gravel contains very little. If you have access to a cycled filter, you can take up to a third of that media and put it in your own filter to kick start yours.