no, neither of them dies, at least not when the story ends. Alan Alda's wife dies and he shows up same time and all and feeds Ellen Burstyn a story about how he is going to marry his neighbor if E.B. won't leave Harry and marry him. He says he can't be alone, but the neighbor knows about the affair and won't allow it to continue. EB is distraught, but won't leave her husband...I think he may be unwell at this point, either way he is too dependent on her (she became a very successful caterer) and she just doesn't think it is fair. A.A. walks out, heading for his new life with the neighbor (debbie I think her name is). E.B. throws herself on the bed crying, A.A. comes back in and thows his stuff down and says its all a lie, he just wanted her to be with him always, but he will continue to show up every year until they are too old or something like that. Lots of tears, hugging and kissing.
Its been a while since I saw it, but that should be it in a nutshell. I always imagined that someday Harry would die too and they would end up together, travelling for some reason. who knows.