I had a similar issue recently, and did various tests. The support of IDNs in email is variable at best.
The character set used in DNS is very limited. So domains with “special” characters are handled using a special encoding called Punycode. These all start with xn-. Applications that understand the encoding can display the special characters as intended, but they will perform things like DNS lookups using the punycode version. If an application is given the non-encoded version, and it does not understand that it needs to encode the domain name before doing a lookup for the MX record you are in trouble immediately.
If the mail clients don’t understand the IDN, then just insert the Punycode in the mail client and that element should work fine. I would not assume that the other side of the email exchange will work if they use the IDN domain. You will also have issues using IDN domains with lots of online services that try to validate the address, and many email clients will not render the display correctly.
With my own IDN domains, I use
[email protected] as the canonical addesss, but I have configured
[email protected]éxample.com to work also, but that requires a second (and in my case a third and fourth!) domain to be registered and maintained. Don’t expect things like
micheá[email protected]éxample.com to work at all.