Encrypting traffic might be taking things a bit far, yeah. I see nothing wrong with encrypting generally, but unless there's a readily-available package to use in order to do away with coding-time, it's probably not worth it in this case. Plus, it'd add another layer of potential bugs, even if the potential is slim.
And yeah, unless the customer ID is used in any fashion player-side, I'd personally prefer it wouldn't be sent, seeing how it's part of a key and all. Sure, it'll always be accessible to people hosting servers (either through packetsniffing or savefile-harvesting), but at least that's just one person and not everyone you play with. Might just be my paranoia speaking though.