While, as @DuckTapeAl has pointed out, nothing in the rules state that fear is mind-affecting, and therefore the RAW answer is "No",
RAI: Yes, undead are immune to demoralize
I found a couple of quotes by James Jacobs, Creative Director at Paizo, in the ">>Ask *James Jacobs* ALL your Questions Here!<<" Thread on the Paizo messageboards. The short version can be found in this post:
[...] Intimidate to demoralize is indeed a fear effect, and thus creatures immune to fear or mind-affecting effects can't be demoralized by this skill
For the longer version, here are three quotes, sorted by date, emphasis mine.
Little Skylark wrote:
Are paladins above level 3 immune to intimidate?
They are immune to being demoralized, since being shaken is a fear effect.
[...] Can you demoralize mindless creatures with Intimidate and/or sway their condition towards you? [...]
This is still a question for the rules boards, but my preference? No... you can't demoralize mindless creatures, because you need a mind to know fear, and you need to know fear in order to be demoralized. The rule of common sense is my rule citation here, in other words.
Malick Rel wrote:
I have seen a few questions recently regarding morale and similar things, and I was wondering if you might offer your two cents worth on an issue of roll vs role play.
There are all manner of creatures out there that are immune to fear or mind affecting, and there are all manner of PCs that can throw down Intimidate and Diplomacy checks that would seem almost magical in their potency.
When an entity cannot have it's mind forcefully changed by a magical effect, are they subject to their mind changing through Diplomacy or Intimidate? Here is where the Role seems more relevant to the Roll, even if it is in the 50+ range.
Would a "successful" intimidate check against a creature with immunity to fear make them shaken?
Diplomacy effects are not technically mind-affecting, and as such you can diplomacy against creatures that can understand you and realize what you're doing. The target needs to be intelligent enough to understand you of course. Intimidate to demoralize is indeed a fear effect, and thus creatures immune to fear or mind-affecting effects can't be demoralized by this skill.
Now there is some interesting disparity in these (which is not unusual at all with James Jacobs rulings). Mindless creatures are immune to mind-affecting effects, which according to the third quote makes you immune to fear, yet he states that this is still unclear and he has no rules citation for this. However, this might just be for the RAW-side of things.
Overall I get the impression that demoralize is intended to be a fear effect, and that fear effects are intended to be mind-affecting effects. But as others have pointed out, that is not really the case with the rules as written.