Will a portable ADS-B unit, like Stratus, meet the requirements for my aircraft to be ADS-B equipped by the 2020 mandate?
The short version is no the Stratus will not meet the requirements, and for several reasons.  

The final rule requires ADS-B OUT (and the Stratus is only ADS-B IN) that meets particular TSO requirements (see below), and portable units will not.

The FAA has an ADS-B FAQ on their website which has a lot of great ADS-B information.

The minimum equipment required to meet the mandate is addressed by:


  What equipment is required by the new rule?  
  
  The rule specifies ADS-B
  Out equipment compliant with either Technical Standard Order
  (TSO)-C154c (Universal Access Transceiver) or TSO-C166b (1090 ES).
  However, to operate in Class A airspace, aircraft are required to
  equip with avionics certified to TSO-C166b.


The FAQ also specifically addresses the question of portable units and says that they will not be allowed:


  Will the FAA allow portable/handheld units, or will they have to be panel mounts only?  
  
  Installed transponders and GPS units must meet certification
  standards. Handheld devices and displays that serve only for
  situational awareness have more flexibility and are not certified
  installations. In order to comply with 14 CFR § 91.225 and 91.227
  aircraft intended to fly in ADS-B airspace must have installed and
  certified equipment. Portable installations are not compliant to the
  rule and would only be usable for receiving FIS-B services for
  situational awareness. The FAA is in the early stages of investigating
  a portable device for glider aircraft.