This is at least incorrect for Akamai and CDNetworks (examples of large CDNs; if you are talking about something silly like CloudFlare, then all bets are off). I run my entire website, most of the content of which is dynamic, through CDNetworks; they definitely maintain hot connections from their systems through to my server, and use it for uncached origin fetches. For more information on related performance improvements, see one of my earlier comments.
Sure, but Akamai is the "big iron" of CDNs - you can run your own custom code in a JVM at their edge locations. So I kinda think anyone in the market for Akamai isn't getting SSL termination advice on HN :)
http://news.ycombinator.com/item?id=2823268