Can CiviCRM handle Extensions in tar.gz format (automated distribution)
No, it does not support tar.gz files -- it only supports zip files.

The relevant logic is in CRM_Extension_Downloader. Note that checkRequirements() and extractFiles() are written to use PHP's ZipArchive.

Update: Another tip. You may want to test that a given file can be downloaded+extracted correctly, but that usually requires publishing a new release (which means that you have publish something untested... oops). To test the download+extract steps before publishing the release, you can do something like this:


Create the zip file and determine its URL.
Run drush cvapi extension.download key=org.example.myext url=http://example.org/myext-test.zip