Let's say that a fictional company, AwSemCo, discovers that a published vulnerability "CVE0day" affects their systems and they immediately start investigating it. They go to the web looking for a solution, what to look for forensically if they've already been hit, etc. As employees at AwSemCo are searching all about CVE0day, their search activity would leave signals in the searches that AwSemCo might be vulnerable to the issue.
Is it possible for someone outside of the search giants to determine what the people at AwSemCo are searching for on Google? If so, is this a viable source for reconnaissance and/or information-gathering?