Is web-presence important for researchers?
The short answer, at least in theoretical computer science, is yes.  Especially pre-tenure.
The Coin of the Realm in academia is fame.  Hiring and promotion decisions are based primarily on the perceptions of your impact by leaders in the research community.  Those intellectual leaders must know who you are, they must know what you do, and they must think that what you do is excellent.  This is precisely why it's so important to network, network, network — go to conferences, visit other departments, talk to visitors, ask questions, answer questions, go to lunch, drink beer, play pool/golf/frisbee/Settlers of Catan, race go-karts, exchange business cards, all that stuff.  Having a visible online presence is just another form of networking.
Similarly, if you want to attract good students, they have to know who you are, they have to know what you do, and they have to think what you do is interesting.
Similarly, if your work is not freely and easily accessible on the web, it is much less likely to be cited than freely accessible work of comparable quality.
To give some personal examples, I have good reason to believe that these web pages were a significant factor in my academic job search and even my tenure case, and this stuff definitely helped me get promoted.  I expect that these pages similarly helped Suresh, and these pages similarly helped David.