The name part, per the standard, is case sensitive. However, some organizations I get email from canonicalize it to all caps - and one even removes the dots(!) and all-cap it, which for my gmail I have a filter that sends all non-dotted email to spam, since 90% of my spam is non-dotted. Since that particular email was important and I'd just happened to notice it in spam, I checked the capitalization change and called them and even managed to get through to speak with their email manager. He absolutely insisted I was wrong about it mattering and said they wouldn't change it.
Changing case could be a co's lazy way of checking for existing accounts. In a perfect world they would store the input as-is and also use a lower or upper func on the indexed col. I suppose if they are verifying emails with their users and not seeing a big drop-off in verified accounts, they probably don't care to be too exact. Removing dots from the user portion is pretty shitty though.
The domain being in any case for the purpose of delivery is part of the standard, but there's nothing I know if which would prohibit you from implementing local delivery and routing in any way you want once the mail is accepted.
You have no guarantee that the domain part case is preserved from what the user wrote, if it's not defined to be case-sensitive. So you can do what you want, but the input data are not reliable.