In my experience, connecting with c-level execs on Linkedin has about the same success level as picking up the phone or e-mailing. Since you have more visibility into the execs work history, interests, and connections, LI can feel like the "magic prospecting pill" when in fact it is just another avenue to try and establish connection.
Whatever ratio you put into number of phone calls, translates to number of meetings, translates to numbers of sales. The same formula holds true for messaging and connecting to individuals on LinkedIn.