Note these draft regulations amending the CIL Regulations which will, from 1 April, enable application to be made for social housing relief by landlords of private rented housing where that housing is let at no more than 80% market rent and to persons in need. A s.106 will need to be in place securing the rent level and the allocation.
As I read these amending regulations, the s.106 does not have to be in place at the time planning permission is granted (as long as it is in place before relief is applied for and before commencement). So it could be done as an afterthought in order to take advantage of the relief. Also, a unilateral would suffice as an "obligation entered into".
The final point to make is that s.106 obligations regulating rent levels and criteria for occupancy are likely to be very difficult to enforce.