Using Drush make to install a profile
Sure.  Take a look at the file drupalorg_testing.make.bootstrap in the drupalorg_testing project.  The relevant part is:

projects[drupalorg_testing][type] = "profile"
projects[drupalorg_testing][download][type] = "git"
projects[drupalorg_testing][download][revision] = "master"


Usually, when building a profile, you will download only Drupal core and the profile in the bootstrap makefile, and put all of your other modules in the makefile that is bundled in the profile.  If you are making a makefile that makes use of someone else's profile, then you may include your additional modules in your top-level (bootstrap) makefile.

If you ever want to move a module from one location to another, you'll want to use the registry rebuild tool.  It will fix up the system table to account for the module's new location.