While there's no easy way that I can think of to make a continual supply of activated carbon or activated charcoal in a long term emergency, charcoal by itself is still a chemical "filter". Though charcoal won't do as good a job as its activated self, I've read an article or two that stated using between four to ten times the amount of un-activated charcoal in comparison to activated charcoal will do a very good job. It's all about available surface area, and that's the magic of activated carbon/charcoal.

Also, you'll want to create as much surface area as possible to run the water through, so break down the large chunks of charcoal into smaller and smaller and smaller pieces.

So, if you're going to boil your water supply using wood, you may as well collect or make some charcoal while you're at it to use as a filter. It's not going to hurt.

Also, don't burn chemically treated woods...