Your question makes me wonder how many people who commit suicide do so with the belief (1) that their consciousness will cease (their identity will end) and how many do so with the belief (2) that their consciousness (and identity) will continue but in a better existence (e.g., heaven). Though this seems like an impossible survey to do (no way to ask the dead!), we could ask people who survive attempted suicides what their goal was (or if they had a goal at all). Perhaps the research has been done. For some reason, I've always assumed that most people who commit suicide (other than terrorists) do so with belief 1 rather than belief 2. And some people may avoid suicide even in the face of despair because they have the belief (3) that their consciousness will continue in a worse existence (e.g., hell), as Hamlet reminds us: "the dread of something after death, The undiscovered country."
Of course, it would not be illogical to say "I would rather be dead" if one believed (2), that dying tranports them to a better world (and "I would rather not be dead" obviously makes sense for someone who believees 3). So, the question is whether it makes sense for someone who believes 1, that his or her consciousness will cease with the death of the body, to say it.
First of all, I don't think it is right to say it is impossible to conceive what it is like to be dead. On this view, there is nothing it is like to be dead. And it seems we can conceive of that--it's presumably the (lack of) mental state we undergo in dreamless sleep (or under anesthesia). We can conceive of it; we just can't experience it consciously.
Now, does this impossibility mean that it is illogical to say "I'd rather be dead"? It doesn't seem so to me. One might mean, "What I consciously experience is so miserable that it would be better for my consciousness to cease." (I hope anyone who feels that way would seek help from friends, family, professionals, and help-lines before he or she believed it to be true, especially since miserable experiences can often give way to much better experiences with time.) If I say that, I am not saying that I will be better off (that things will be better for me) when I lack consciousness, since I will no longer exist. Rather, I am saying that things will be better when I lack consciousness and no longer exist. (It's easy to see how there could be utilitarian arguments for suicide.)
Another way to see the point is to recognize that we have current preferences for states of affairs that we know will exist only after we are dead. For instance, I prefer there to be a viable environment for my great-grandchildren. And I am willing to give up satisfying some of my preferences for my current self to satisfy that preference (though we really are not built to do so and it's hard to get ourselves to do it!). I also put away some of the money I could spend on stuff for me to purchase life insurance, which I know would only be useful if I were dead. I prefer that my family have that money even though I believe that I won't experience them using it. Similarly, it seems one could prefer to have no experiences at all to having bad experiences, even though one believes that he or she would not experience having no experiences.