For the majority of communities, the act of 'friending' someone makes no difference upon their level of participation.
These are some exceptions. Communities based around the follow feature, for example. You have to follow people to see anything in these communities.
These are rare.
For most communities, trying to encourage people to add each other as friends is a waste of time. If you can remove the feature, remove it.
It will come as no surprise that real friendships aren't developed by such technical innovations. They come from frequent shared contact, shared history/activities, and reciprocated self-disclosure.
Sadly, for academics, these are more difficult to study.
On October 29th to 30th, the world's top 250 community professionals are going to SPRINT in San Francisco. Will you be one of them?