Most filters work by using a mechanical barrier, of various designs and configurations, to remove PARTICULATE matter down to some minimum size (which again varies based upon the filter design and configuration).
Some filters employ activated charcoal to remove certain dissolved and/or miscible chemicals from the water.
The first aspect wouldn't work. I'm guessing the second wouldn't do a complete job.
If this worked using common backpacking filters, it would be common knowledge by now.
Distillation (e.g. a solar still) would be the way to go if you're serious about trying this (Great shades of Herbert's Dune!!!). Search the Forums, DrJ and i had a semi-humorous exchange on this very subject a month or two ago. He's a wild man!!!
BT, you're a FUNNY man!!! Good one!
True story, over three decades ago in a Senior Level Food & Diary Microbiology course, we were learning about bacteria that spoiled dairy products, such as milk. Part of that learning involved "organoleptic" analysis (using one's senses to distinguish between spoilage caused by different bacteria). Taste was involved (using a pipette to obtain a small volume of spoiled milk and then transfer a drop or two to one's tongue). One particular organism was set aside by the Prof. for me to try, as he figured that no one else would dare. This particular sample was to be the finale of the our taste testing, starring "yours truly". That sample of milk was spoiled by Streptococcus fecalis (take special note of the first two syllables of the specific name - guess where that little bugger normally inhabits in a cow!!!). My reaction was quite instantaneous - fortunately there was a water fountain (or bubbler) across the hall from the Micro-lab. To this day, though i haven't had the great displeasure of performing organoleptic analysis again, i could still tell you if S. fecalis was the bugger that spoiled some milk. Makes an impression. What one does to further science (ok...ok...what one does to get an 'A')!!
So, go ahead and give Ben's suggestion a try. I'll pass on this one. Actually,...i think everyone ought to pass on this one too.