Is it possible to do a Drush make custom installation profile?
You can use the OPTIONAL ATTRIBUTES

root_element[first_key][next_key] = value


  The 'projects' attribute is where you define the modules/themes that 
  are to be packaged with the profile. The first key is the short name 
  of the project (as seen in the drupal.org/project/{projectshortname} 
  URI).
  
  These projects are defined using the short form definition. You can
  use this form if you only want to declare the version of the
  project. The version is the value to the right of the core Drupal
  version in a full version string. For example, if you wanted to
  specify Views 7.x-3.1, you would use:


projects[views] = 3.1



  For pre-releases, like CTools 7.x-1.0-rc1, use this format: 


projects[ctools] = 1.0-rc1


  You can also specify -dev releases of projects; however, this is 
  generally NOT recommended, since it results in end users getting 
  different sets of files at different times that distribution is 
  built, which can cause confusing bug reports. If you really must use 
  a -dev release, it's better to specify a Git revision (see below).


projects[media] = 2.x-dev


Reference


Full example drupal-org.make file.
Managing Drush make files for an installation profile.