Is it possible to migrate customer passwords during Magento migration & upgrade/downgrade?

Yes, it is. The passwords import is supported for Magento Upgrade, as well as for data migration to Magento. To check the full list of Source carts password migration is supported check Cart2Cart Password Migration page.

To import the passwords to Magento you’ll need to install free Cart2Cart Password Migration plugin to the Target Cart. Click the links below to find out more info on: