This depends on what sort of filter you're using. The purpose of an undergravel filter is to supply oxygenated water as a constant flow to the gravel. This means that the whole gravel bed forms a light coating of nitrifying bacteria. Because it has such a vast surface area, this makes it an effective biological filter but due to its poor mechanical filtration it should not be used alone but in conjunction with a power filter.
If the tank you took the gravel from was running an undergravel filter, it probably does contain nitrifiers and will therefore speed up your cycle. However if you AREN'T running an undergravel, there is no point at all to scattering it over your own gravel. Any bacteria present will die. Place it in your filter, preferably next to the biological media (bio balls, bio rings or small porous rocks.) It's probably best to put some of it in your main filter even if you are running an undergravel.
If the tank you took it from wasn't running an undergravel there is probably little or no bacteria on it. you'd be much better off getting some filter media. Sponges and wool might do something but their effect will be less than taking one or two bioballs or biorings or biorocks. Anything that's small and porous and has constant water flow will end up covered in nitrifiers.
In fact you are more likely to get unwanted stuff from both. There is some toxic stuff in gravel which can be released when disturbed.
