
You learn something new every day.
Client wanted to offset the Full-Text Index searches onto the Read-Only Replica of an Always-On Cluster.
Wasn’t too sure exactly how to go about it, but did some research and came across the below MSDN article which mentioned the exact thing I was after:
“full-text indexes are synchronized with the secondary databases”
https://msdn.microsoft.com/en-us/library/ff878253.aspx
So all I need to do is install the Full-Text Search feature on the Read-Only replica and Full-Text Searches will be conducted on the Read-Only replica with no further configuration needed.