Same errors happen with or without punycode. Here are the specific, likely bogus Gmail error messages:Message not delivered
Your message couldn't be delivered to test@lisäämyyntiä.com because the remote server is misconfigured. See the technical details below for more information.
IDNs are messing up Gmail. Other email clients don't give errors when sending emails to punycoded IDN:s. Also the email server works fine and relays, bounces and accepts email from Gmail to all non-IDN-domain without any problems.550 Please turn on SMTP Authentication in your mail client. mail-ot1-f47.google.com [126.96.36.199]:46638 is not permitted to relay through this server without authentication.
I reported this issue to Gmail, but as they don't have a proper error reporting tool, I don't really expect them to do anything to fix this.