That depends. The Pro version of WP All Import will do automated imports from a URL. If you have a way to automate export the other DB to an XML or CSV file then it can be used to run automated updates using crons.
I have a site for one client that cannot do automated exports and instead they need to manually do the export and upload the CSV to the site. I have 2 crons running on this site. Every 5 minutes the first cron runs and it looks at the file to see if it is new. If the file is new then this cron triggers WP All Import to run the import /wp-cron.php?import_key={$IMPORT_KEY}&import_id={$IMPORT_ID}&action=trigger' and records the file time of the csv in a text file for the next check. The second cron is set up to also run every 5 minutes and is set to the WPAI url to start running the import. This call is ignored if the import has not been triggered by the first cron.
This same setup could be used for an automated export as well.
