First, I want to get a little bit nit-picky about language, and then explain my nuanced "yes" answer. No site is exactly going to "regain" their former situation, and that's because Panda is integrated into the algorithm. It's not going away.
So the situation is that a site might see traffic levels that approach or pass their former levels, because the Panda-part now scores their quality as good. It's not impossible (theoretically) that a site could get the Panda boost that was introduced in Panda 2.
Good backlinks were one of the factors that a site I mentioned earlier achieved. And I don't mean a couple of runs with xrumer, either. They shifted the layout so that content was obvious right when the page loaded, they eliminated some questionable UGC, and they reached out to other sites in various ways (including social media) and let them know about good new content - and that got them some new, stronger backlinks.
They are a heavily scraped site. Not only that, but their UGC had (and probably still has) some copy/paste duplicate content from other sites. And with Panda 2.1. their total traffic is now right around pre-Panda levels, after dropping by about 40%. Alexa, Compete and similar sources of competitive data do not currently show that traffic rebound, but their own server logs so, and so do their ad impressions.
The traffic increase has a different configuration or shape than their pre-Panda traffic did, but it's real traffic, real people.
Did the new backlinks "cause" the improvement? Cause and effect are hard to pin down when you make diverse changes all at once. But the new backlinks are a real part of the picture in this case of a real recovery of traffic.