You have to have a decent plant mass for this to work.
To have no water movement at all, would have to be determined by the inhabitants and types of plants. some fish need water movement to be happy. Some plants grow too slow to do well without water movement to remove sediment and discourage algae growth. A good cleanup crew would be essential too (shrimp and a moderately small snail population). People mention water movement for nutrient dispersal, but I think an active fish population can help provide that. Nutrients aren't being depleted that rapidly in lowtech tanks.
I wouldn't recommend this though for tanks that don't get observed frequently. Just setting it up and leaving it to its own devices could be disastorous for the inhabitants.
NavyBlue, FYI fish don't actually put out waste from their gills (other than CO2). Gills are strictly for breathing. Look up the osmotic process, which is where GH and KH come into play for proper hydration and expultion of waste for freshwater fish (for salt water too, but salt water fish actually drink water constantly and also use the process to regulate internal salt content)