HAVING A EMAIL ADDRESS IN UPPER CAPS IS A REALLY BAD IDEA. USING THEM AS "EMPHASIS" IS SOMETHING FROM THE TYPEWRITER ERA WHERE YOU DID NOT HAVE OTHER OPTIONS.
Sorry for that.
As commented by others, an email address is case-insensitive, the domain system is. in some extreme cases, YouCouldUseCamelCase use of capitals. They are used on long words. But choosing a long word as the first part of a public email is also a bad idea.
Sometimes could be necessary for a domain name. FreeDomainNames.Example.com
The truth is that you should drop the idea now. Even in the comments, you have the idea fixed in your mind even after technical arguments
I'm sorry but this relates to a flyer I'm designing.
No, you are not designing your cell phone cover where you can use unicorns if you want.
You are potentially confusing customers, potentially preventing an email to arrive and messing around with the client that also do not like it. There is no single argument to keep thinking about it.
Change size, change the font, change thickness, change weight, change the kerning, put an outline, put a bullet, put an icon, put an explosion, put a hologram... you have options.
There could be some argument if the client wanted to do that. But this is not the case.