Outside of custom-designed software, I don't think this is possible.
I don't believe Facebook groups have automated greeters for each approved comment.
But a little bit off-topic, Colin, you're definitely on the right track marketing to Facebook groups.
This is how I generate quite a bit of traffic for some of my websites and some of my blogs, and that's amazing.
It's all about community loyalty.
And the great thing about it is when people like your content, they don't think twice about sharing that content.
Not just on their own personal Facebook wall but also on other groups, they're members of.
The key is to build on stuff that you know will get passed on or shared.
Make more of those and less of posts that don't go anywhere.
It takes quite a while to get the hang of things.
But once you get the ball rolling, the momentum is nothing short of amazing.