Great Question. The short answer is that they can't substitute an NPS score, rather they are a great complimentary metric.
How do NPS and Social Media interactions differ
Let's use the Facebook like feature to compare against an NPS survey. With the NPS survey you are given the opportunity to register a vote on a scale. If you hate the service you will provide a low vote (and so forth). The Facebook like feature is more of a passive interaction then registering a formal opinion.
The decision to mark a “like” action also varies dramatically from user to user. Some users will literally “like” everything that they are presented with regardless of their disposition towards the product or company. Other users who may love the product or company may simply never be presented with (or notice) the prompt to “like” a page. Even further there are still lots of users that never use Facebook and see no value in interacting with it's features.
How to use NPS and Facebook Likes
Your NPS survey and Facebook Likes are complimentary then. Let's assume that you have a rather high NPS score. However you get very few likes to your Facebook page. There could be many reasons for this. The simple truth may be that while your customers enjoy (and promote) your product to friends and family, they simply do not want information about your company showing up on their timeline. As a user, do I really need my lawyer, dentist, accountant, stock broker, gardner, pool guy, as well as all the clothes brands and stores I shop at posting on my timeline? The truth is that I am just not going to be “liking” all of those even though I may think that I have the best dentist, the best accountant, etc…