If I sent a bag of rice to the bottom of the ocean and brought it back, could I eat it?
Depends on the container.  The bottom of the ocean has three main properties that would affect the rice:


Water 
Salt and floating materials 
Pressure - at the bottom of the Mariana Trench, the pressure is 1000x that standard atmospheric pressure at sea level.


Rice is absorbent.  Depending on the container, if it is permeable to water, then both seawater and pressure will affect the rice.   

Rice + Water = soggy rice with a different texture than cooked rice.

Rice + Brine in Seawater = soggy rice that absorbed salt and fine particulate materials from the surrounding water.  (Cooking this would probably taste just like using seawater to cook rice.)

Rice + Intense pressure = the water, salt, and other materials would be absorbed on its way down more quickly due to the increased pressure, and any air within the grains would be replaced with water as the grain is compressed.  

I do not believe it would work at all like a pressure cooker does due to the cold temperature; I am fairly certain that it would be only the grainy soggy rice - cooked rice is different from dry rice because of changes to the starches by the heat when cooking (and obviously the absorption of water).  The rice itself is a starch, so the carbohydrates would not likely respond differently to the pressure in the absence of heat.  

I am curious if anyone might come up with anything on the chemistry of carbohydrates under pressure at near-freezing temperatures - whether any chemical bonds may be altered (like deformation of the beta-1-4 glycosidic linkage).  That's beyond my level of chemistry/physics knowledge.

But the duration of the journey would likely result in mush by the time it came up.  There are not many nutrients to white rice in the first place, other than the carbohydrates, so the nutrient change would be what it gains in the brine.

If I am missing something, please point it out.  But I believe this is the extent of the effects on the rice.

However:

If your rice were in a sealed container capable of withstanding the pressure without collapse or leaking, I am fairly certain that the rice would arrive back to the surface completely unchanged.  Humans are able to go down to the sea bottom in specially designed vehicles.