Not a very good idea, I used to work for PUR water filters so I know a fair amount about these. Too little filtration surface would mean frequent clogging. They will typically filter in the 25-75 micron range, but you want to be in the 1-10 micron range to filter out yeast and sediment. Plus there is actiavated carbon and sometimes ion exchange resin in residential filters. Not good things for wine as flavors may be stripped or altered.
I think if you go through the normal process and rack one extra time, it will come out brilliantly clear. My parents whites are always crystal clear. I have a feeling it won't be hard for us to do this, once we move into whites. Racking and time are your friend.