No, IMAP push does not work for disroot with iOS devices. And yes, it looks like the Apple Push Notification Service needs to be contacted in order to get it working.
The folks at mailbox.org have develped an open source plugin for dovecot: https://github.com/st3fan/dovecot-xaps-daemon. However, I don't which server software you guys have deployed. If you use dovecot as well, it might be worth checking out