The quick answer is no. If you had a filter with a strong enough flow to actually capture everything, no fish would be able to tolerate it. But you wouldn't want to either, for the health of the biological system.
Biologically speaking, in most aquaria the substrate is the most important "filtering" area, more-so than the filter itself. The prime duty of a filter is to mechanically filter particulate matter out of the water. Biological filtration to help clean the water will also occur, it can't be prevented. But the filtration processes that occur in the substrate go beyond this. Nitrifying bacteria (dealing with the ammonia/nitrite issues) is only one aspect; there is a host of various bacteria living in a healthy substrate.
In some of my tanks I dig into the substrate in the open areas with the end of the water changer, and in other tanks I rarely if ever do this. Each tank is biologically unique, and the depth of the substrate, tank size, fish load, and live plants all factor in.
Byron.