Can drush make fetch dependencies for a newly added module, without using it to build the whole site?
Yes, it is possible. Just run the makefile on the current codebase, and specify --no-core option from the drupal root:

$ drush make --no-core sites/all/modules/mailchimp/mailchimp.make.example


Here's the log of a test I did:

$ drush dl drupal
$ cd drupal-7.28/
$ drush dl mailchimp
  Project mailchimp (7.x-3.1) downloaded to /tmp/drupal-7.28/sites/all/modules/mailchimp.

$ drush make --no-core sites/all/modules/mailchimp/mailchimp.make.example
  Make new site in the current directory? (y/n): y
  Beginning to build sites/all/modules/mailchimp/mailchimp.make.example.
  libraries-7.x-2.2 downloaded.
  mailchimp downloaded from https://bitbucket.org/mailchimp/mailchimp-api-php/get/2.0.4.zip.

$ ls sites/all/libraries/
  mailchimp
$ ls sites/all/modules/
  libraries  mailchimp  README.txt


If any of the projects/libraries declared in the makefile already exists, it will be overwritten.