That would depend on your definition of success, but I think they're doing quite well.
Paper.li is a 5 month old news aggregation site driven by social media. It helps you publish a daily (digital) newspaper with content drawn from sources you follow on Twitter or Facebook. It doesn't use the tweets, though; instead it uses excerpts from articles linked to in a tweet. The process is largely automated is largely automated and the result looks something like a newspaper.
It's been a while since I last looked at paper.li, and I can tell that they've improved their layout system. I have to say that I find it a lot more visually appealing now than when I saw it last back in September.
My interest in paper.li is twofold. I look at it as a possible way to gain readers, and I also look at it as a way to find new information for my readers. It's not very good at either task yet, but that doesn't mean this won't change in the future.
Right now I'm seeing about 5 times as many visitors from Twitter as I am from paper.li. I'd say that's good; paper.li is probably less than a fifth the size of Twitter. It's also less than 5 months old. But neither site is a major source of traffic so it doesn't really matter.
On the other hand, I've spot checked the more popular newspapers on paper.li. They're really not getting all that many page views. It's hard to measure the daily traffic but the lifetime traffic for the popular newspapers isn't all that high considering some have been running for 4 or 5 months.
My other interest in paper.li is as a source of info. But at this point it is still less useful than Twitter or my RSS feeds. Yes, I really am looking to replace RSS feeds; RSS is a slow way to get news. A post might show up in a feed 6 or more hours after it was published. Snicker if you want, but a link to that post will show up on Twitter within a minute of publication. Also, the news in the post often shows up on Twitter before the post is published. Seriously, in spite of it's many technical failings Twitter really is the best real time source for news. Paper.li, on the other hand, is only published once a day so any news it has might be as much as 24 hours old. That's simply not fast enough to suit me.
But that "daily newspaper" aspect is still useful. I wish I'd thought to use paper.li while in Las Vegas for CES. I didn't have time t check my Twitter feed but I might have had time to glance through the aggregated content.
I actually have a third reason to watch paper.li, but it's a little odd. I track all the new content sharing platforms (like paper.li) because I want to be ready when a replacement for WordPress comes along. I like WordPress and it's a very good platform, but there are a lot of smart people out there messing around with platforms. If a better tool comes along I want to be ready for it.
It's a little early to say yet, but this really could be the next big thing. Before it can do that, though, paper.li will need to find a way to break away from Twitter and Facebook. It needs to stand on its own; otherwise it will stay an appendage of the bigger sites.
P.S. I have a paper.li newspaper based on my Twiiter account: