In blunt trauma, yes. However in response to tissue damage the blood pressure drop is due to vasoactive cytokine release, allowing immune cells to migrate to and respond to localized damage. However when the damage is widespread, widespread vasoactive substances are themselves the cause of blood pressure drop via vasodilation and vasopermeability.
Beyond that, damage to the microcirculation, the capillaries, venules, arterioles, and veins near the surface would also cause a blood pressure drop from sheer mass blood loss. The blood may be contained in a limb (although in this case I assume it will leak out into the water freely), but the blood is no longer in the circulatory system.
The massive insult would also set off a massive norepinephrine/epinephrine/endoprhin response that would also blunt some of the pain signals. Although once the damage reaches the dorsal root ganglia, assuming the person is still conscious, that would be worse pain than anything at the skin. Then again, I'd assume complete uncosciousness by that point.
There are other factors to consider as well. Widespread tissue damage will cause a massive release of substances such as potassium and magnesium, which will interfere with the heart beating and the brain processing. To the point that, in not too long a timespan, you just won't be conscious and/or your heart will go into afib/vfib.
http://www.medbullets.com/step2-3-dermatology/20554/burns
http://www.totalburncare.com/orientation_burn_shock.htm