How long it may take to establish a sufficient colony is a function of a number of things. It can be done in as little as a few days or as much as many weeks.
Now lets talk bacteria and how much you will have in the normal tank. And the answer is, over time you will have exactly the amount it takes to handle the bio-laod of the tank. And this number will be reached no matter what type of filter you use, what is in the tank etc.
When you run a new filter or media in parallel in an established tank it does not create more bacteria, at best it spreads them out. bear in mind that the bacterial colonies will be the largest where ever thet can find the best supply of water bringing them food, oxygen and carbon. When you take a sponge out of your filter, drop it into the tank to settle where it may and put a brand new sponge into the filter here is what will happen.
Because the old sponge is no longer in the optimal place, the bacteria will not do as well nor reproduce as fast. However, the new sponge in the filter is now an optimal home and some bacteria will finds its way there. So two processes start to work together. In the old sponge the bacteria conditons become less favorable and the amount of bacteria living it will decline while the new sponge begines to see a concomitant increase on bacteria.
While pretty much no bacteria are moving from one place to the other as if they packed their bags and moved to a new home. They "recolonize" by how they reproduce at each location. More and more will be in the new sponge and less and less in the old.
For whatever reason, some fish really do best being added to a 6 month old tank versus a brand new one, even if its fully cycled. There's more going on than just ammonia oxidation...
