that's quite a difficult one. It's not as if you've got water to test for ammonia/nitrite/nitrite. Of cause after four weeks bacteria would start colonizing the media and I would imagine there will be quite so lot of bacteria present. However, it's difficult to say how much bacteria you would have to sustain the amount of fish you have in your new tank. It really does depend on how many fish will be in the tank once you put the filter back on it. Now from a personal point of opinion, four weeks is not enough time to build up enough bacteria to sustain any more than a few small fish. If you're going to leave it for four weeks, you might as well leave it for six or seven weeks.
Once you put the filter on the tank, you would need to constantly keep checking the water for ammonia. Obviously if you get to the end of the week and your ammonia nitrite are still zero and you have a good nitrate reading, you know that you have successfully established a biological filter.