Sure, but it needs to know that there are new messages. I don't think that's a separate permission on any (e.g.) ActivityPub/XMPP/IRC server implementation today.
On all XMPP server implementations I've worked with, the push notifications mechanism supports (and usually defaults to) not including any message body in the API call to the push server. Usually it's also possible to leave out the sender name/JID, e.g. with prosody's mod_cloud_notify.