Does peeling potatoes before boiling them actually increase the amount of water they absorb?
Cook's Illustrated "New Best Recipe" Book in their dissertation on making Mashed Potatoes used several methods: peel &amp; dice, peel &amp; whole, etc.. and the 'best and most consistent' results achieved was by boiling them whole then shocking them to cool (put in an ice bath) and then peeling by hand (grip in two hands and twist). 

Having used this technique for several years I will say you have received good information. Less water, but still soft and fluffy...and most importantly 'tasty' (IMHO).



Ok, so it's a couple of days later and I finally have a moment to catch up to this. From Cook's Illustrated "New Best Recipe" Book pp.186-8 


  We started by peeling and cutting some potatoes into chunks...while
  cooking others  unpeeled and whole...even when mashed with identical
  amounts of butter and half-and-half...and salt...The potatoes that had
  been peeled and cut made mashed potatoes that were thin in taste and
  texture and devoid of potato flavor. Peeling and cutting before
  simmering increases the surface area...through which they lose soluble
  substances such as starch, proteins, and flavor compounds , to the
  cooking water. The greater surface area also enables lots of water
  molecules to bind with the potatoes' starch molecules . Combine these
  two effects and you've got bland, thin, watery mashed potatoes. The
  potatoes cooked whole and peeled after cooking yielded mashed potatoes
  that were rich , earthy, and sweet.


(note: If you can pickup a copy of this book, it is a treasure trove of useful kitchen information)

In short it isn't just water absorption (water into the potatoes) that makes them weak, but also what the water removes from the potatoes into the water (and then down the drain) which will produce disappointing results.