I think that there is no definitive answer to this - I believe that there are good arguments either way.
Personally, I'm using the "must die to be awakened" as a concept in my currently in-progress fanfic, The Rise of Evil. I just wrote chapter four, in which Ganondorf, in his quest to be evil rising faces the Sage of Forest (an original character for the story - since it's set in a made-up, non-canon era meant to be somewhere in the "gap" between some of the canon games). This whole "death to be awakened" came up for my Forest Sage.
In canon...
I think there's a lot of evidence for it in Ocarina of Time. As said, every Sage went into their respective temple to acertain what was wrong and/or to fight the monsters within. Considering how grueling those places were for the Master Sword-wielding Chosen Hero, and the fact that he encounters them in something of a mystic state, it makes perfect sense that in order for Link to "awaken" them, and for them to give him their full power, they'd been killed by the beasts of the temples. As far as remains go - well, the bosses of those temples *are* monsters. Can we say... burp? (Okay, so maybe Koume and Kotake would have just incinerated Nabooru or something, but still..) I think good evidence is also given by the fact that Rauru is as he is. I recall him telling Link something along the lines of his body having long decayed away while he remains in the Chamber of Sages. (Is this just in the manga or in the game? I haven't played OoT in a while). They also seem to be represented by motes of colored light and have other spooky, spirit-type properties.
However, in The Wind Waker, the Sages of Earth and Wind seem to be *powerless* because they are dead and in need of specifically *living* Sages to take their place. -- Perhaps this serves to refute the "Sages are dead" in OoT entirely, or, perhaps, the Wind Waker age simply had different rules regarding the Sages, in need of "living" powers rather than "dead" powers to charge the Master Sword.
It is an enduring mystery.