How do you measure the quality?
If the blog network is a niche blog network, almost every blog will give more value than a a general blog. So I can believe there will be results with mere one blogpost.
But when it comes to general blog networks, one post doesn't help much. You need at least 5 contextual posts to see some decent ups in rankings.
There are only few providers who actually work on strong backlinking of these blogs (under networks). Fortuntaley, we do promote and build backlinks for our blogs in networks but still, 1 post from a a general blog cannot give noiceable results.
It would cost a lot if all 200-300 blogs of a network are build up with that high quality so they start giving results with 1 post. And if they do, contextual services would be way too costly. Hope all makes sense.