Should I mention strong engagements on the CV which are not related to the domain I want to get in touch with some professors for PhD applications. Thus I will send them my CV and I am wondering if I should mention achievements and engagements which are in general strong, but not related to the domain of the PhD. (I want to do a CS related PhD)

E.g. organizing conferences, McKinsey distinguished, Delegate at International Relation conferences, Banking Conferences, etc.

Is it beneficial to mention it or in contrary even counterproductive?
Such details do not seem so counterproductive. In fact, it shows your versatility and that you possess effective communication skills. 

To avoid blurring achievements from your primary domain, you may add a separate Ancillary Achievements or Other Accomplishments section.