The filter you are using is not designed to handle the temperature, or pressure, that is involved in the cooling system. Using it to remove contaminants and then tossing it is probably not going to cause any major issues, but I would not leave it on there for any significant length of time.
I personally don't think that coolant needs to be kept as clean as oil, but on this site that may be my opinion alone. I've never had a breakdown or overheating situation related to "dirty" coolant and I leave mine in there for the maximum length of time indicated by either the car manufacturer or the coolant manufacturer. I converted my 89 Accord from OEM type coolant to Dexcool in 1997, started going 100,000 miles between coolant changes, and had no problems. Changing the water pump is part of the timing belt service on that car and I never saw any gunk or buildup there or in the radiator.
There is such a thing as overkill.