HI,
That sounds a bit misleading.
The iMessages servers can tell when an "new" device is added to the Apple ID and will start sending it the iMessages that are being sent back an forth form that point onwards.
If a device has been Off line such as a Home computer that is Asleep or turned Off then the iMessages servers will attempt to "Catch up" the iMessages it has missed.
This does presume there was an "start point" for the syncing to that device and that the the time differences are not too long.
If you Saved the Chats on the Mac and these are part of the Back up you made then you may have older chats.
Open Chats (because the saving only works on closing a Chat) will not be saved by this method.
Broadly speaking I would say that the Mac will not be seen by the iMessage server as a device that has been Off line and that iMessages will therefore NOT resync to it.
10:08 PM Thursday; November 15, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously