No. It would need to specifically state it bypasses the ability to get past their immunity.
The mesmerist can also partially affect such a creature with his mind-affecting spells and abilities if it’s under the effect of his hypnotic stare; it gains a +2 bonus on its saving throw (if any), and if affected, it still has a 50% chance each round of ignoring the effect. Ignoring the effect doesn’t end the effect, but does allow the creature to act normally for that round.
I think the bigger hurdle is that intimidate is a skill, not an ability. 'Ability' normally refers to class or race granted abilities, not skill use.
I would agree that "spells and abilities" includes skill checks. There are several specified types of abilities (e.g. spell-like abilities or class abilities) but the term itself is very broad and can describe almost anything a character can do.
As the Psychic Inception grants you the chance to ignore a creatures immunity to mind-affecting effects and thats the only thing stopping you from demoralizing undead or vermin you should be good to go. Of course they still have a 50% to ignore that condition each round.
Hey look, another thread on this subject.
I would say the mesmerist could use intimidate, it is a mind affecting ability. Possibly the only skill that is.
The problem here is that intimidate is a fear effect, and the mentioned creatures are immune to fear effects. I would have to check each one seperately to be sure they call out fear though.
I also think abilities refers to special abilities, but it might be worth an FAQ for that.
I was incorrect. Fear is not called out except for very few creatures as a specific immunity, and nothing says it is a mind affecting by default.
Per this FAQ, intimidate is a mind-affecting feat effect.
I thought it just said it was a fear effect, but in that case it won't work since the named creatures are immune to mind effects.
Skill: A skill represents a creature's ability to perform an ordinary task, such as climb a wall, sneak down a hallway, or spot an intruder. The number of ranks possessed by a creature in a given skill represents its proficiency in that skill. As a creature gains Hit Dice, it also gains additional skill ranks that can be added to its skills
Thus skill is an ability
Psychic inception allows creatures immune to mind-affecting to be affected by them. It doesn't do anything to fear immunity though. It would allow you to intimidate a spider for example.
I see the first sense was chopped off in the above comments. That is what threw me off.