The answer is a firm yes then.
(It has been a while since I was involved in chem, so forgive me being "rusty" (geddit) )
Dynamites are mixtures which may be either described as "the stuff is crystallised together and is pretty much a compound" or "stuff is a mechanical mixture, where components loosely retain their original properties". Perhaps they even add an emulsifier to keep things together. I have no idea about where dynamite fits into the continuum. But it probably starts off at 1 and ages towards 2.
Unless the lump of stuff is porous, the water will not get into it to aid separation. Then we get into the realms of things like pores in it, whether or not the surrounding "stuff" likes water or not, etc, etc. I guess it's probably at this sort of point that we realise an experiment is necessary.
Perhaps another compound separates out. Who knows what size the particles are, how they are mixed or what the stuff is like. I'd say that it's probably pretty damn irrelevant.
The facts are:-
1. There is AN in some dynamites.
2. The stuff which sweats is NG and this causes headaches by being a vasodilator.
3. It's probably still quite dangerous.
My reasoning for NG sweating would be that the "stuff" which isn't NG crystallises/rearranges itself to exclude the NG which is probably in a colloidal form.
Sorry to be awful, but the teacher in me points to:-
http://www.pyrosociety.org.uk/forum/topic/2134-hydroscopic-hygroscopic-or-neither/ Not to be confused with "deliquesent" which is where stuff absorbs water from the air and becomes a liquid itself. :smartass:
Edit:- Water of crystallisation could be another culprit. Rearrangement of "stuff" where water is an energetically favourable thing for the compound to associate itself with. The possibilities and chemical pathways are considerable.