The amount of 'fresh' water trapped in the two icecaps is enourmous. So yes, many areas will get far more rain than they do now.

I know there is a concern that the current CO2 levels far exceed what has been measured in the gases trapped in deep icecores... but we have no way of knowing how those 'trapped' gases behave over hundreds of thousands of years... so we may well be comparing apples to oranges...

Lastly... there's no predicting if the global warming will ever really come to be. All it would take is one exceptional eruption of a volcano, ala Krakatoa or Pinotuba, or even Mt. Ranier, for example... and the ash added to the air could counter act all the greenhouse gases in the course of a decade. Many historians are coming to believe that the Dark Ages in Europe were so named... because they were indeed "dark!" ... the results of some impressive geological activity.