Is it possible to export arbitrary configurations?
For some of the configurations/settings that aren't picked up by the Features module, there is the Strongarm module.

Strongarm gives site builders a way to override the default variable values that Drupal core and contributed modules ship with. It is not an end user tool, but a developer and site builder tool which provides an API and a limited UI.
An example of such a variable is site_frontpage. In Drupal this defaults to node, which ensures that the front page gets content as soon as some exists, but for many Drupal sites this setting is simply wrong. Strongarm gives the site builder a place in the equation - an opportunity to set the site_frontpage to something that makes sense for their site.

At the time this answer has been posted, the Backup and Migrate module wasn't yet compatible with neither the Features module nor the Strongarm module. See Make backup profiles and schedules Features exportable, (closed as fixed on May 6, 2013) for what exactly the issue was and which branch fixed it. The bug report doesn't contain any patch: The code has been developed in a branch different from the branch for which the issue was opened.