Hi,
I have not found a limit for a size of file in Chat or Messages when using the AIM Service.
Jabber accounts can vary as in some cases and third party app is needed to "turn on" File Sharing services which can be listed as a separate service.
I have not tested specifically with iMessages.
As the iMessages servers are separate from the iCloud ones I not sure any iCloud email limit is going to apply.
(Messages on the iPhone and the Mac obviously makes use of Contacts and these can be synced via iCloud and possibly your Apple ID in Messages is an iCloud one but that is as close as it gets.)
There maybe limits when the Contact is not on a wifi network and is receiving data via their Service Providers Data contract (as in when it converts to SMS)
8:49 PM Tuesday; June 18, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.4)
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