It is a popular misconception that an increase in demand coupled with an increase in price is sufficient to make a good a Giffen good. This is false.
First, the good must be inferior (demand decreases when income rises), which search advertising is probably not. Second, the increase in demand must be because the income effect (the increase in price acts like a decrease in income, so you will buy more of the good since it is inferior) is greater than the substitution effect (you will buy less of the good because its price relative to substitute goods increased). It's not clear this is the mechanism at work here.
Just because an increase in price causes an increase in demand doesn't make search advertising a Giffen good. This is a necessary, but not sufficient condition.
One could argue that search advertising is "inferior" to brand advertising in the sense that it produces low-margin transactions and builds no brand loyalty. Companies do it because they have to, in the meat-and-potatoes sense. In the long run, loyal users created through a brand are more valuable.
Also, the increased spending on SEM does come from a limited marketing budget, so there is a definite income effect.
Finally, Google keeps changing the SEM rules in ways that that result in price increases, in addition to the auction effect.
Thus it would seem that all the Giffen good conditions are met.
But still, search advertising isn't an inferior good in the traditional sense. All else constant, if a company gets an additional dollar of revenue, they won't spend less on search advertising in absolute terms.
When I came to the part about google, funnily enough, it reminded me of Paul Graham's "What the Bubble got right", specifically about Yahoo in Para's 2 & 3.
First, the good must be inferior (demand decreases when income rises), which search advertising is probably not. Second, the increase in demand must be because the income effect (the increase in price acts like a decrease in income, so you will buy more of the good since it is inferior) is greater than the substitution effect (you will buy less of the good because its price relative to substitute goods increased). It's not clear this is the mechanism at work here.
Just because an increase in price causes an increase in demand doesn't make search advertising a Giffen good. This is a necessary, but not sufficient condition.