Can UV cure inside opaque or more massive printed object? From what I understand, UV curing of resin prints works by starting a chemical reaction that hardens the resin permanently.

Also, a curing step after print is needed to speed up the print and also to reduce the curing during print, which would cure resin beyond the current layer.

However, what is the transmissivity of UV light in partially cured prints? If I print a more massive object, or if I use an opaque resin, how deep will the object harden properly? Absorption is always exponential, meaning that it decreases quickly with depth.

Depending on the resin, how thick prints can be effectively cured? This information is not provided with the resin, which I actually would expect from reputable manufacturers.
From what I know about the various resins, once they are printed they are cured enough. Some of the transparent ones require additional curing, however the manufactures of the machines only test based on the max size that their machines can print. 

The resin never stops curing apparently, going into diminishing returns; curing slower and slower as time goes on. Only way you will know for sure is by experimentation. You should get a poly-carbonate tube, place black tape along one side then spray paint the rest black. This will leave a window that you can use for future observation. Seal the bottom, and pour in uncured resin. Leave it under a UV source for 2 weeks then peal the tape off to see how much of it has cured. Then come back here and ask Trish to do the math on what the co-efficients of absorption are for the material :)