Mushrooms are already about 90% water - so how much more could they absorb from a quick washing? Harold McGee was curious and did an experiment to find out (ref p 182, The Curious Cook) - and Alton Brown took it a little farther and demonstrated it in episode number EA1H22 of Good Eats - Myth Smashers. AB didn't note much difference between 5-minutes vs 30-minutes of soaking. These are Harold's results:
He took some (23) mushrooms (Harold is frugal - so these were probably just common white button mushrooms although he didn't specify) and weighed them (252 grams = 8.889 oz). He then soaked them in water for 5 minutes, blotted off the water on the outside and weighed them again. They now weighed 258 grams (9.10 oz). So, on the average, each mushroom absorbed a whopping 3.75 drops of water!
As a mushroom grows up through the earth - only the top and sides of the cap, and the base of the stem, come in direct contact with the "dirt". The gills on the underside don't. By soaking the mushrooms, some moisture might be absorbed via the stem (depending on how fresh they are - and if you trim the base of the stem off before soaking), and some moisture is probably trapped between the gills via capillary action.
If you are going to eat the mushrooms raw then "maybe" you could taste a difference (bet you couldn't unless the water was really funky) but they would not be waterlogged - but if you're going to cook them it's a moot point since they will release their moisture.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain