Can I upgrade plugins via FTP?

Short answer: yes you can upgrade your plugins via FTP.

  1. Download the new version of the plugin.
  2. Disable the plugin you are about to update.
  3. Upload files over the top of the plugin.
  4. Re-enable plugin

If the plugin is written well stats, settings and options should remain intact. As Rarst has already mentioned the automated upgrader just overwites files.

The reason for disabling the plugin first before upgrading is to stop regular site visitors running the plugin while files are being uploaded. If a plugin is run with only half of the correct files in place things can go wrong such as errors popping up and settings getting corrupt. Hence why you should disable the plugin first. When I say disable I do not mean delete.