I think 4E took that route when ruling that some powers did damage on a miss. It makes sense from the perspective that hit points don't really represent physical damage.
As I said, it has to be true even from the first issue of the game.
A person is basicaly hit by hitting an AC 10 (there are natural defense modifiers, like DEX, but let's leave those out of the discussion for a moment for simplicity. It won't change the point.) That's the way it was in 1st edition AD&D, and that's the way it is in 3.5 d20.
Any number rolled higher than that is really "penetraion" against armor.
So, if a character is hit by rolling against AC 10, he's hit at that number no matter what. Armor might make him AC 15, but the AC 10 roll still hits him. It takes a roll of 15+, though, to avoid/penetrate the target's armor. Therefore, attack throws of 10-14 are hits that do no damage.
Or, you can call them "misses", even though they hit.
Is there any sort of attack that deals damage on a miss in the Conan RPG?
No, it operates like 3.5 d20.
An example of when an unsuccessful attack throw represents a complete hit (and therefore actually causes damage)?
What we need to do is define what a "hit" is and what a "miss" is.
1. Hit - a successful attack throw that does damage.
2. Hit - the character is physically struck by his enemy.
3. miss - a non-successful attack throw that does not do damage.
4. miss - an attack on the PC that does not do damage.
Let's use definitions 2 and 4.
So, there are hits that clang off the character's armor (a successful hit that does no damage--represented by a failed (or miss) attack throw.