The Batch API won't continue running if the browser is closed correct? Can a batch be run with Drush? Can the batch API continue to run once the browser closes? If not then can I run a batch with Drush? I have an insane amount of data to migrate and I don't really have time to wait for it to import every item one at a time on my local machine.

Currently I have my batch process setup to import each item (groups, users, blogs, files, etc) one per op call. But I am going to change that to do 50 to 100 per call to improve the speed. But I just ran it last night on just my groups and it took almost an hour to run on almost 800 groups.

This is part of a data migration from multiple websites to one unified site. Thoughts? Suggestions? Can Drush help me out?

EDIT: I have rolled my own export/import scripts for this because of the nature of the migration (multiple Drupal 4.7 sites that are highly customized and with potentially hacked cores to Drupal 6). I already have the exported data file created and ready to go. I am just testing the import portion of this madness.
It seems possible, have you tried: Processing batch jobs with drush.