Although I have gotten many replies to my inquiry whether fungi undergo apoptosis, they fall into two general categories:
1. Let me know if anyone knows the answer.
2. Fungi are unicellular (false-many are coenocytic, many differentiate complex structures of different cell types) so of course they don't undergo apoptosis.
Just to add to the excitement, it was pointed out to me that Ausubel, et al, published a description of programmed cell death in plants that dances around the question of whether plants undergo apoptosis in the same sense that animal cells do.
So, I guess this question is still open, and I think it may be relevant both to developmental processes (like protoperithecium develoment) and to use of antifungals in therapy.