I'm not sure this will answer your question completely, but earlier this spring I took my filter out of service for the first time in 4 or 5 years. The water is noticeably cloudier with more suspended particulates than in recent years. In years past I had crystal clear water with glass -like visibility to the bottom which was 3' below. If you have it, I recommend using it. If not, one can do without in my experience.

Hi
Have run an above ground 5x10x3 deep pool since 82 with no filter though I do use a purge system as it was built as a storage for rainwater but evolved into a water garden.
Recently had to do some repairs but returned to no filter lol though this time I'm keeping goldfish not tropicals. kept the purge but added a long narrow overflow. The plants have completely covered the surface in less than 4 weeks so clear water doesn't matter much lol gary

do your self a favor and install the filter.the filter is the most important part of the pond and a lot of people go cheap with it. if you dont install the filter you will wind up with a cesspool. i have and over size filter and have had over 100 koi in it.my water is gin clear.i am down to about40 koi now.

In my experience the filter is important for suspended particles, which may come and go, but floating plants go a long way for keeping the water clear and free of green algae. not only do they out compete the algae for nutrients but they also shade the water from the sun.

Seems like most water gardeners define a filter simply as a "filter". Green water, add a "filter". Cloudy water, add a "filter". Got suspended particles, add a "filter". Got ammonia, add a "filter".

In aquaculture, sewage treatment, high end Koi ponds, etc., there is no concept of a "filter" as a generic, fixes everything, gadget. In these cases results are highly desired, sought and performance is measured and debated.

This isn't at all the case in water gardening. "My water is clear and I have a filter, so therefore my water is clear because of my filter" is the extent of measurement. A debate...forget about it. Dare to say a certain filter is not as good as another and you'd think someone's kid was insulted.

Filters are not important in water gardening because it's OK if water isn't clear. I mean no one likes it, and people love to complain about it, but not to the extent of actually learning about filters, how they work, or installing one, at least for the most part. If the fish in a water garden die it's very sad, but not so sad to stop another trip to the pet store for a another $2 worth of feeder fish. When someone has $20,000+ worth of fish, or the health of fish impacts a person's income...filtering becomes a VERY important subject.

With that kind of standard in water gardening I think it's completely hit or miss, just a guess, as to whether adding a filter to your pond would yield some undefined result. It depends more on whether you'll willing to "see" some result whether real or not.

If you want the pros and cons of having a "filter" you first have to define what it is you want to filter out.

If you have ammonia the pros of adding a bio filter is that it would convert the ammonia and you wouldn't have to do water changes, binders, or replace fish every few months. The cons of adding a bio filter to a pond that never measures any ammonia is added expense, complexity, maintenance, and loss of yard space without any benefit.

If you have suspended particles or you want to limit suspended particles in the future the pros of a mechanical filter is that it would lower suspended particles. The cons are expense, complexity, maintenance, loss of yard space, and the very real risk that it wouldn't work at all. Especially true if the mechanical filter design comes from the water gardening world where filters aren't tested, they only have to sound good.

Same basic deal with green water, cloudiness from clay or tannins, etc.

I have an upflow biofilter made from a 45 gallon pvc barrel and a prefilter around my submersible pump. The amount of gunk that collects in the pre-filter and the biofilter indicates to me that the filter is needed. Not only that, my pond only goes green for about a week in early spring which goes away about 3 or 4 days after I get the filter running. So, you probably want a filter.