Not directly. But it can have an effect, even a large effect.
Basically, how you link through your website affects not only Google's ability to spider, but how it sees the hierarchy of your website. Linking prominently to an article that has high "shareability" will improve it's overall position in the search results. This means more people see it. The more people who see it, the more people are likely to share it. As they share it, you get backlinks into your website.
This then means that the people who saw those widely disseminated articles are given the opportunity to look at other content on your website. That can then get shared, giving you new backlinks to other content on your website.
So, while a link on your website won't in-and-of-itself boost your article up the rankings, it can play its part.