The purpose of your list is key, and although I'm a 'seen only' guy for my personal life and year lists, like you I would absolutely record heard-only birds if I was putting the data out on eBird or Birdtrack, as you are aiding knowledge of all the birds which occur on that site, not just the ones you've seen.I don't really count my list totals much as the amount of birds I've seen total doesn't really matter, I'm more of a patch guy. I doubt im ever going to be travelling the world or even the UK for birds. Maybe that will change one day, who knows but at the moment im not much of a twitcher. There are lots of "common" birds in nearby places that I could probably go and tick off whenever I want but just haven't bothered. Most of my birding goes on birdtrack, and I'm more into the recording data for the local area sort of thing, and just hope that a local rarity turns up now and again to keep things exciting.
So I almost feel like the records aren't really for me in a way, though I do get excited at a new patch tick or new highest flock count or whatever.
So I will record heard only (though obviously depending on the bird that could be really disappointing). And would record dead (and report it).
When undertaking a breeding bird survey hearing becomes more important than seeing species, since you are recording the number of individuals proclaiming territory as an aid to estimating breeding density.