First, the web is only a system of hyperlinked documents which can be browsed by a man or a machine. This means that the web is only information, and as far as

First, the web is only a system of hyperlinked documents which can be browsed by a man or a machine. This means that the web is only information, and as far as I can tell information is not intelligence. A system capable of using this information may be intelligent, but not the information per se. So, maybe the internet will evolve to a "superintelligence". But this leads us to my second point. From the verb used in the question, emerge, it looks to me that this "superintelligence" is reached without human intervention. But as spontaneous generation does not exist, we need a system capable of evolve, without external help. And as far as I know, nowadays, neither the Internet (network) nor any of each nodes can evolve without human help. So, until somebody invents an evolving device and connects it to the Internet, my answer is no.