Sorry, I don't have an iOS device, so I'm not sure. The only mention I could find on the website was: https://www.migadu.com/guides/gmail_android/

> While Gmail is an IMAP client app, it will not check for new mails continuously. Not only it does not support IMAP Push extensions which are standard nowadays, but the [most] frequent polling interval is 15 minutes

Which I guess implies they offer IMAP push, since they're expressing disapproval that the Gmail app doesn't support IMAP push