They weren't trying to kill themselves. They were trying to make the tank dirty so that they'd have to be taken out of it and Nemo could escape. Yes. That's the point in the movie.
In reality, if the tank was that dirty, there would be MUCH less oxygen, thus sufficating. Also, the ammonia would build up and poison them.
And if those fish are like goldfish, if the conditions were bad enough, they would try to jump out of the tank to get away from the grim.
Shari Lewis: Did you ever wish upon a star?
Lamb Chop: I once asked Mr. Rogers for his autograph.