As Tom said, any transactional change (a change described and mediated by BI and AI notes) made to the source database while OE Replication is active will be propagated to the target, as the AI notes are streamed from the replication server process on the source system to the replication agent process on the target system. The agent applies the transaction notes to the target DB.
I'm not sure where you heard that but you can still back up your source DB successfully when replication is not in sync.
Welcome to PT! I suggest you start with the PDF documentation set for your OpenEdge version. Start at
this site and you can download the entire set of documents in a zip file. There is a whole manual dedicated to OE Replication. I also suggest reading the Database Essentials and Database Administration manuals. The former contains some generic database concepts which you can skip if you know the material, and then it gets into specifics about Progress' implementation of those concepts. Both manuals will be helpful for understanding concepts like the before image and after image files which is essential for using and understanding OE Replication.
Other material that may be helpful:
From BravePoint Virtual Interchange 2010:
Gus Björklund, Progress Software/Dan Foreman, BravePoint
Practical Progress OE Database Internals (contains a good high-level overview of how the BI works)
slide deck
video
Tom Bascom, White Star Software/DBAppraise
After Imaging, The DBA's Best Friend
slide deck
video
Adam Backman, White Star Software/DBAppraise
OE Replication - Your Options Explored
slide deck
video
From
Progress Revolution 2011:
Rob Marshall, Progress Software
Demystifying Progress OpenEdge Replication
slides/audio
From
PUG Challenge Americas 2011:
Adam Backman, White Star Software/DBAppraise
OE Replication Made Easy
slide deck
Also, if you're able to travel to the Boston area in June, be sure to attend PUG Challenge Americas 2014, the premier Progress technical conference of the year. Three days of pure technical sessions and workshops with no marketing fluff, for one low price. And a special deal on on-site accommodations! Book now for early-bird pricing.
http://pugchallenge.org/register.html
If you're not in North America, there are other conferences you can attend from time to time. PUG Challenge EMEA happens in Dusseldorf this year in November. Details here:
http://www.pugchallenge.eu/