Yes it can do. you may also see a rise in green water and blanket weed due to the excess nutrients

you could get a filter but with no tiny aquatic creatures being swept in the filter there will be nothing to eat the algea and the pond will turn into a green soup,then you would have to put another filter for that and that leads to diffrent problems. the best thing is to have sand or gravel under the bottom and put rocks on the sideds of the pond to stop slit and soil getting in. if you want soil on the bottom to plant the plants then just plant the plants in pretty pots or baskets of soil then have the rest of the pond filled with gravel. trust me pots look nice underwater.

I plant my plants in clean gravel tied in with nylon fishing line. they then root as normal and take nutrients out of the water.
Fish also like to exfoliate in mud so perhaps they are stirring up the compost as they swim against it. You could lift the baskets and cover the surface with clean gravel or pebbles. they can still rub but wont stir it up.

if it helps it will settle in time [2-6weeks]. you can buy a product [cant remember its name] that causes the particles to flocculate and sink to the bottom of the pond.

The nutrients may cause an algal bloom and that will also clear in about 4-8weeks with out any treatments.
The more you 'fuss with it' the longer the problem lasts.
The water suddenly clears as if by magic in just a day or two after weeks of murk.