As long as you choose plants that do well under low/moderate light, there's no reason why a non-co2 tank can't work. People who can't keep a non-co2 tank or think it's impossible, lack either the patience or knowledge required and shouldn't be taken all that seriously.
Your big issue here is your plants are in a crippled state to start off with. This will take a lot of patience, pruning, work etc. to overcome. Stick with it and you'll get there.