No, the P1 only filters sediment. You need a carbon filter for the chlorine.
Here is a 1 micron filter that filters sediment down to 1 micron and contains carbon. This filter is the same size as the P1 filter you mentioned - approximately 10" L x 2.5" wide.
http://www.waterfilters.net/Pentek/wholehouse/Carbon_Filters/CCBC-10.htm
Thank you,
WaterFilters.NET