In theory, only if you can find the right combination of plants that will absorb ALLl waste products generated by the fish, and fish that can get the needed balanced diet from feeding on only the plants.
In other words, if you can set the tank up as a closed system (think Biosphere 2
http://en.wikipedia.org/wiki/Biosphere_2) you could avoid PWC. But as you can see if you either know about or read about Biosphere 2, a closed system can be more difficult to maintain than an open one where you do PWC.
I think the most likely result would be that for a long while, everything would go ok, but unseen to you, conditions would slowly deteriate. But at first, the fish would slowly adapt to the slow deteriation, until finally, you suddenly start losing fish as the lack of maintainence eventually leads to unhealthy fish and they eventually die.
[Time to embarass myself]
As a teenager, not knowing what I was doing and not knowing anything about fish, accidently did an experiment. I had a gold fish in a 5 gallon tank. There was no heater, no light (except what came through the bedroom window), no filter, and not even a substrait in this tank. Initially, changed the water when it got to looking dirty and I feed him once in a while. But as time went on, the periods between feeding and water changes got longer and longer until finally they both just stopped. Eventually, the ONLY maintainence and care this fish was given was to add water to the tank to replace what was evaporating (and even that came from the catch basin from the dehumidifier in the next room I was responsible for emptying). So eventually, this goldfish became an alage eater (must have, because I wasn't feeding him), and his waste must have been getting converted back to alage. This poor fish survived under these conditions for over two years. Then suddenly one day, this fish (that can live for more than 20 years when properly cared for) died at an age of about 3 to 4 year old. The point being, I setup a basically closed system, it kept the fish alive, but unknown to me, the conditions were harming the fish and eventually lead to his premature death.
BTW, yes it was horrible what I put that fish through. But now I know better. Today I once again have a goldfish (actually it belongs to by son, but given his age, I'm the one that has to care for it). This time, the goldfish lives in a 20 gallon tank with 3 rosey red minnows, snails, and shrimp as tank mates. The tank has a filter, air stones, a thick sand substrait, and several plants. The tank is well lit, the fish are feed twice a day, occationally with peas to aid their digestion, and gets 10%-20% weekly PWC. In four months, the goldfish has grown to twice the size that other goldfish ever became after 3 to 4 years.