You mean the aeration holes, correct? I would say yes. It doesn't look like this guy does though.
http://containergardening.wordpress....em-larry-hall/
I guess it would probably depend on the size of the container you are using above the gutter. I can't see how the extra aeration for the roots could hurt you.
What are you going to grow? It would appear to be a good system and utilization of space for greens and herbs. Would love to see your setup when you get it done.