Good God, no. Do not ever try that. Britas and the like are just a charcoal filter. The boiling requirement is to kill living organisms small enough to pass through any physical filtration. When they say boil it, don't try to go around the process.
No...they are not small enough to pass through any mechanical filtration. Several kinds of filter exist that are able to filter out even the smallest pollutants (viruses) which are much smaller than the bacteria which are the concern with the boil water warning.
That said, for the wrong reason your advice is correct. If you don't know you have one of these filters...you probably don't. Boil your water...
This is not good enough...
http://www.purwater.com/#/faucets
This is...
http://www.envirotechproducts.com/omni-water-filters/omni_filter_model_ot32.htm
and so is this...
http://www.amazon.com/Katadyn-Hiker...e=UTF8&s=sporting-goods&qid=1187204358&sr=1-1