The answer to this particular question is yes, and at the same time no, Let's take a fearless paladin for example.
If you try to intimidate a paladin, no matter how hard you try, no matter how many natural 20's, dazzling displays, and plus modifiers you have to your intimidate check, you will never scare, terrify, shaken, etc a paladin.
However! You CAN use intimidate in more ways than just scaring someone.
An example of using intimidate as a fear tool would be...
"Fear me foolish Paladin! I am the grand master of all evil draco-liches and lord of the 9th plane of hell! Flee before me!"
At this, a paladin wouldn't even flinch from fear. He's immune to it after all.
An example of using intimidation, without trying to scare the paladin.
"Oh, so you're the paladin everyone's been talking about. Tell ya what, "chief", you go back the way you came or else me and my army here will attack and raze that innocent town, killing everyone in our paths!"
The boss saying something like this would make the paladin think twice. The badguy is using a show of power to intimidate the paladin into backing off, but not by scareing him.
Basically, this is the difference between threatening the thing immune to fear, or threatening something the thing immune to fear would care about. Taking a hostage, if you will.
It's not the robbers the police are afraid of, it's the hostages they are threatening to kill that the police are worrying about.
