The longer it's stored outside, the more spoilage (nutrient loss) you are going to have...that is a given...left out long enough it will eventually get to the core.
Basic "theory" nutrient loss of hay IN DRY STORAGE....Majority of loss comes during "curing" process...curing in the field and in the bale. In the field from resperation/inclimate weather. In the bale is goverened by moisture content of the hay when baled...the higher the moistue content when baled the more chance of heat damage and nutrient loss you will have in storage. Once the curing process in the bale is over year to year loss is very minimal as long as it isn't exposed to moisture.
So, a rough answer to what you are asking is yes...as long as moisture is made availabe to the bale it will wick or sponge moisture into the bale until eventually it is a rotted heap of junk. (But should make good compost) I can't recall totally accurately to be 100% correct and am talking about barn stored hay, but from memory, tests show you can figure 1.5 - 2% nutrient loss the first year with the majority of that coming in the first 3 months after baling. (maybe someone that tests in the field may have experience here, I test in late fall after the cureing process is complete). Again this is directely related to field conditions and hay condition at the time of baling. Minimal loss, less than 1/2% the next year and very negligable losses after that if stored in a dry environment. Add moisture anywhere along the way and the game changes.
PS...yes, even barn store hay stored in contact with the ground in a dry environment will have at least some damage related to direct contact with the ground.