When cutting for myself, if I run into a dead tree, it goes into the same pile as the fresh ones. Once I use it, whether it be for the OWB or the epa, it is noticeably lighter in weight, but never rotten.
We've been cutting the ash since the borer moved into our place in 2002. Needless to say, all our trees have been dead for quite some time. We simply keep on stacking and don't worry about when it was cut or how dead it was and just always burn the oldest the firstest. We're still cutting that dead stuff and have way too much of it. A lot of it will end up going to wasted.