What option is better? Will group admins still see a private account as real one (don’t see why not, many people have it set to private), will it decrease group approval rate? Any other cons?
Private, but with couple of public posts 
That’s how most of real accounts look like.
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Yeah, i think private group with couple of public post can make new member more curios what is inside.
I think OP was referring to FB profile and how to make it look more realistic.