Tony Hsieh of Zappos has a team of 4-5 full time email handlers I think. Part of the image/Zappos culture is openness though- so I'd guess that some other execs as mentioned in the question might not have the same volume of email from external parties.

Fun fact, I think their official titles are Email Ninja.

I learned this from being lucky enough to have a one hour sit down with him and some of my bschool classmates on a trip to Vegas last year.