Generating Error when data size is larger then max text repl size
The SQL Server error log only captures errors having a significant severity (generally 19-25, with exceptions). See the documentation here:


https://docs.microsoft.com/en-us/sql/relational-databases/errors-events/database-engine-error-severities 


Imagine if all divide by zero, ambiguous column, or syntax errors flooded the error log? That log would quickly become an unmanageable mess. 

What you can do is use an Alert, which can trigger notifications and other actions whenever an exception with a certain severity (or, in your case, error number) is raised:


https://docs.microsoft.com/en-us/sql/ssms/agent/alerts


For example:

EXEC sys.sp_add_alert @name = 'repl size error',
  @message_id = 7139, -- I believe this is the right message
  ...


See this doc for sp_add_alert usage:


https://docs.microsoft.com/en-us/sql/relational-databases/system-stored-procedures/sp-add-alert-transact-sql