If Registered devices cannot be reached the iMessages Server(s) keep trying until the iMessages are accepted.
It could be viewed that they are "Offline" messages as it appears that they are the same as the way AIM used to do things
The Server are continuing to "Push" the messages at the devices when there are some to Send.
Mail tends to work on your App fetching any email from those emails server you use.
The difference is that once the iMessages are accepted by the devices the item is deleted from the Servers.
This means new Devices cannot get older iMessages.
IMAP mail server require you Trash items you don't want. Until then any new device can Fetch the emails from the server.
7:29 pm Friday; March 16, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)