If this actually happened with key web properties (e.g. ALL NewsCorp papers, or Twitter, or NASCAR/NFL/etc exclusively on one search engine), I predict it would turn into a land grab which would ultimately just lead to segregation. However, the key question in my mind is:

Would users follow the sites they trust OR find new sites via the search engine they trust?

I'm guessing people would use the search engine they trust to source new information and then visit the sites they love (which have been excluded from their search) as a destination (i.e. going to WSJ.com direct and then searching content there)...

Google would still remain the No 1 search engine but WSJ etc would then have to rely more on their active user base. Not a smart decision for Mr Murdoch in my opinion.