No - is the the short answer.
The Agile manifesto came about through a bunch of folk with different lightweight development processes coming together and finding common ground (you can read about the history of the manifesto for more info).
My google-fu is failing me but I think a at least one signatory of the manifesto has been asked this question explicitly in the past and have said "no" (Ron Jeffries or Kent Beck I think...).
The "customer" that the manifesto talks about is the person who requests the software be developed - not necessarily the end user.
The "individuals and interactions" are primarily the stakeholders and the product development team - not necessarily the end user.
You're certainly not the first to notice that there are commonalities though. To some extent, I guess, you could say that the agile manifesto is an approach to making the process of software development a better experience.
That isn't to say that Agile development approaches aren't good for UX. Many people (myself included) have found integrating UX practices into agile processes a very effective way of approaching developing successful products. The Agile focus on feedback and collaboration provides many more routes for UX folk to have a huge impact - many more than more traditional waterfall approaches.
Agile is great news for UX as far as I'm concerned - but not because it's based on UX principles. You might find this UX Matters article on Agile UX Design a relevant read (bias warning: I'm one of the contributors ;-)
For me Agile & UX are peanut butter & jelly. Great by themselves. Even better together.