I don't know if any funded scientific research has been conducted (don't know an oganization the would fund this), but there are loads of empirical data fom hobbyists and professionals alike. Rock, being porous, has the capability to absorb nutrients if kept in a high nutrients environment and due to diffusion, th nutrients will leach in a low nutrient (ie. Our tanks) environment. So, a rock obtained from an area (for example) with high levels of runoff could collect nutrients from fertilizer or pollutants and if concentrations remain high enough for a period of time, yes, it can leach inorganic nutrients.
With live rock, in particular, the nutrients are typically a result of organisms living on the rock. When we get live rock, typically it is exposed to air for a period of time. While many organisms can tolerate this, a great many cannot (sponges are particularly succeptible to this due to air getting trapped in the spicules and preventing future water flow through). Decaying organics release nitrogen and phosphorous along with a number of other compounds.
So, I don't have a study to cite, but experience and a number of biology and Chem classes can back it up.