Can the Powered Up app be used to directly control the Boost Move Hub?
As of the Powered Up app version 3.0, this is possible.



Old answer:

As of August 2018, this is not possible. However, TLG has stated that they plan to add more compatibility to the Powered Up system, and this will likely be available as a firmware update in the future:


  Q. Will all different Powered Up components (Boost, WeDo, Train, etc)
  be able to communicate and control each other, e.g. running a Boost
  program sequence using a Powered Up hub or using sensors with Powered
  Up hubs?
  
  A. It is the aim that the Powered UP platform will work together
  across both with the wired and wireless connection. Some of these
  connections are not implemented yet and will come through firmware and
  app updates.