Once a Boil Water Notice is announced, it effectively means, that the water is being considered non-potable, at least temporarily. Therefore, these filtration systems cannot be used.

There are additional types of filtration and treatment systems designed for use on non-potable water. When properly applied, installed, maintained, and operated these systems can bring the water into compliance with the Safe Drinking Water Act (SDWA). Such a system might be used to purify, for example, water from a lake. If you have such a system, then the water might be safe to use, depending on the contaminant that is causing the Boil Water Notice.

Does boiling the water produce any other effects?

If there are high levels of other in-organic contaminants of concern in the water, then boiling might slightly increase their concentration due to the evaporation of some of the water during the boiling process.