That is a very good theory except you forgot about one part. It takes around 5000-10000 micro particles to clump together for filter material to catch it. The only way it can do this is to be sent back into the tank/pond and circulated. Dead micro particles of algae are no bigger than the living ones, and your filter does not catch the living ones.
Everything I have ever read about pond keeping/uv sterilizers tells you to go filter then UV.
In fact I have never heard of anyone going UV then filter. In some models, like mine, the inside is ridiculously hard to clean and if that gets jammed up with poo and other aquarium waste it is going to be a pain in the butt to clean.