No. The dividends are less than 1% of the share price. For it to be considered to be profitable on dividends alone I think it would need to pay 10% or more. I don't expect it to increase by 1000%. http://investor.apple.com/faq.cfm
In classical stock markets, if Apple is worth $450 a share and they issue a $10 dividend after trading closes, the next morning the stock will trade at $440. If you grew up reading the stock listings in things called "newspapers" sometimes you would see a letter (I think "x" for "ex-dividend" but it's literally been decades) in the listings next to stocks that were doing this, so you knew that a price drop was about to/had just happened.
So even if no one were engaging in arbitrage opportunities, it would make no difference when you purchase the stock.
Alternately, we have this market. Apple went ex-dividend today, which would (ordinarily) result in their opening price being adjusted to 2.65 below yesterday's closing (457.26). In this (real) market, it opened up somewhere between $2 and $5 (459-463). (google's data isn't very fine grained here).
In a 100% rational market, all this excessive cash is accounted for in current stock price, and price of stock will drop as dividend is issued -- they most definitely will.
Apple's stock is already priced to account for their war chest. If the war chest is drawn down, the stock would (presumably) reflect this and drop in proportion to the amount of cash that's released.
That is true, however it is not why the/a stock market is irrational.
Well, first off, one person asked, the other told, but in your sentiment:
What you refer to is more likely a skew of information, a mix of information traders and (e.g.) value traders, or (generalizing term) noise traders.
There may not be a facit as to "Is this good or bad for the value of AAPL to have dividends paid out in this amount?". There may be different interpretations. Some might feel it's a sign of a new path in dividends payout from Apple even in the future. Some might think it's a short term "stunt" to keep the investors happy. Some might think it makes them less valuable as they have less money, some might think a strategy of catering to profit and investors will outweigh the "loss" in dividend payout.
Just looking at this thread of comments shows there are many interpretations.