Hah, blast. Just when you think you have an interesting new idea... Certainly not using google gears would be a good idea, though.
It's crazy to think how much power a major site like Google could harness if they actually did this. If I were them I'd do it, but make it opt-in, of course.
If it weren't for the same origin policy they could make a distributed web crawler that loads web pages, parses them, and returns a nice clean list of words and links for the real heavy duty processing. They would need some assurances that clients didn't tamper with the data. Perhaps several clients could process the same pages, and they could ensure they match before accepting the data.