From a game standpoint, sure. From an RP standpoint, I don't know how my character would know that. When you look around at your fellow party members, and everyone is either untouched or lightly scratched - nobody has sustained an injury that will persist through rest - then it's hard to despair. If you don't know that the encounters for the day are calibrated to test your exact limits, then it would be hard to know that your specific degree of HP loss (fatigue?) is something that you need to worry about.
Maybe there's a way to look at HP loss and Hit Dice and all that, such that it promotes in-character thinking that parallels what the players are thinking at the table. Whatever that may be, I couldn't figure it out, and that's what prevented me from being able to RP when playing 4E.
HS in 4e is equivalent to "health" in action movies.
In action movies, even if the guy has bleeding feet (lost HS) and no shoes, he's still able to dodge, he's still able to climb, when the fighting starts, wounds are forgotten (full hp) - he
performs. The hits they take during the scene, that make the hero dizzy and miss, and bleed everywhere, and that make you think : "damn! that hurt! - Is he going to make it?" Those are hp - and once he gets a breather, they convert to HS : still as banged up, but able to go for another round of abuse.
When you look at your buddy with full hp and 0 HS left, that dudette is bleeding all over, arm broken in two places, and tapped to a stick. But she's still got the fire to mess the bad guys up. She'll headbut that orc and she can take a few more shots... but not to many... it's getting close to a death-scene potential here.
In 4e hp, are not meat - HS are meat (actually, they
can be meat, they can also be hope, faith, etc.) It's almost a direct translation of a boxing match : hp are what you have for a round, HS are what you've got for the
fight.
You can't tell me you don't see a difference in a boxer's face/stance/everything between round 1 and round 8.