The question is, what other filtration methods do you have in your tank? Do you have a sump with a skimmer? Do you have a lot of live rocks in your tank?
You need to understand the basis for DE's advice to you - the bioballs were put in to create a large surface area for bacteria to colonize. These bacteria convert the most harmful substances in your tank - ammonia and nitrite - into less harmful substances - nitrate. Your tank will then begin to slowly rise in nitrate concentration. This will eventually become harmful as well once the nitrate levels reach very high. The only solution then would be to do a major water change in your tank.
The removal of bioballs is to prevent this from occuring, because dead particle matter tends to get trapped in the bioballs and slowly decay, polluting the tank. Once you have no bioballs, the detritus or "rubbish" will collect at the bottom of your overflow compartment and can easily be removed. You should try to siphon this out as often as you can, as this is decaying matter which is pollutive. This is why most people have "clean" overflows, in the sense that there is nothing put into the compartment. No bioballs or anything except filter wool. This is to facilitate removal of detritus.
Nonetheless, without bioballs, you will still have to deal with the buildup of dangerous ammonia and nitrite. This is less of a problem in a mature tank with a lot of live rock, as the good bacteria would have colonized these rocks. In a newer tank, you will need to supplement the bacteria (which is still growing) with other mechanical filtration methods, the most important of which is the protein skimmer.
If you intend to keep marine fish, a skimmer is a MUST. If you don't know what a skimmer is or don't have one, I suggest you approach a local fish shop to learn more. You can check out some of the sponsors of this sgreefclub site.