Well, manual bans actually don't show the "email" thing - they show "Please contact Riot Support for more information" as in this picture http://i.imgur.com/dwH2XBX.jpg
I know it's not the right year - and some of them don't show a year, but that's what they'll say when they're manual (or if it's a manual chat ban it may show the 14/perma message with the "We can't display your chat logs at this time, contact support" message).
The ones I know for sure don't send emails for security reasons:
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Obviously if an account is compromised, you don't want it to go to the wrong email and let the hacker know you know its compromised.
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I have seen yes and no on chargeback - I guess it depends on severity maybe, or some other security related issue (maybe if an account has chargebacks because they're hacked it doesn't send?)
OTOH, bans for third party programs, MMR boosting, etc. all send emails.