Mechanical filtration may not be as imporatant in a planted tank since your gravel contains most of the bacteria, and plants can break down waste to nutrients, however weekly maintanence and vaccuuming is still important. Mulm build up can result in death of plant roots, and benificial bacteria which will throw off the balance.
In most planted tanks water flow is very important. This constant movement helps nutrients, CO2, and even heat spread out evenly throughout your tank. Areas that don't get much flow tend to build up debris and are usually areas that you see algae growth popping up. At night plants use oxygen and give off CO2, so water flow and aeration is important.
Beaslbob's explaination is good but does not quite work as you think with some chemicals. Suppose the ppm is constantly going up faster than you can remove it. Lets start with that 100ppm scenario and lets say that by the end of each week it goes up 20ppm. If you do a 10% water change each week here is what you get:
Week 1: 90ppm
Week 2: 90+ 20= 110ppm (10%) = 99ppm
Week 3: 99+20= 119ppm (10%) = 107.1ppm
As you can see week after week the ppm amount can go up, or if you remove more than 20% a week has the potential of going down. Chemicals in your tank can still go up or down due to the balance of fish to plants. The nutrients for plants can become limiting as they all grow, however if you have fast growing fish and slow growing plants, you may see nitrate and other chemical going up faster than the plants can use them.
Sometimes the water change itself is adding the substance. As water evaporates from the tank you top it off, adding more substance that doesn't get evaporated (often hardness). A lot of high tech planted tanks have to add various nutrients to the tank in order to keep the plants healthy. They add nitrate, potassium, phosphate, iron,...etc because the plants are using this stuff up faster than a normal water change can add it back in. However, when using the "lazy" method they reset these ppm each week by doing a very large 50% or more water change.
Long story short, it can be done but you have to keep in mind that unless it is a completely closed off system like an eco jar, you should still test the water paramaters at least every few weeks or months and adjust your normal water change as needed. Watch to see how your plants and fish are doing, and know some of what is in the new water you are adding. Fine tune your lighting, hours on, etc.
One of the better self-sustaining setups uses "mineralized" soil as a substrate. This means you should not have to feed your plants for years, but you still have to do normal water changes and test your water from time to time.
