Here's the Baby Irish Chain I just completed ...
http://www.quiltingboard.com/picture...h-t213094.html
If you look closely, you can see that I did the diagonal quilting, just on the chains.
You will need to watch your batting requirements for quilting spacing, as this does leave large open spaces.
Of course, dependent on the size of your chains/blocks.
If it was too large an area, then you could put a motif of some sort in the open area.