There is a way that accounts can be suspended without sending a moderator message.
If an account is deleted or destroyed using two specific options (with either spamming or "no longer welcome to participate" marked as the reason for the deletion), the system will automatically levy a 14-day suspension at the same time the account is deleted, with no corresponding moderator message. Normally, this automatic suspension isn't visible to anyone, so this doesn't matter...
...unless the user recreates the deleted account, in which case the system will automatically "reinstate" this suspension, as part of an automated process to reinstate suspensions against accounts in case the user tries to delete and recreate their account to avoid it. This can lead to an apparent case where no moderator message is sent.
Additionally, chat suspensions don't carry a moderator message, as that's an entirely separate mechanism.
Other than these cases, and the case of network-wide suspensions pointed out by Catija on a deleted answer here, all site suspensions do indeed carry a moderator message with them.