No. Pressero does not store the actual plain text passwords for site users, but stores a hash of the password that is calculated using various values. It is not possible to recover the actual plain text passwords for any users on any sites.
The password hashes are unique to the site the user is on, and the same user with the same password on two different sites, will have different password values stored for that user. This makes it necessary, if duplicating a site to reset the passwords for the users on that site. This can be done manually for the users individually, and can also be done by using the functionality for importing and exporting users.
You can access the import and export functionality by going to User Management for that site, choosing Site Users, and then clicking the gear icon at the top of the user list. Choosing Import/Export Site Users will show that window. Clicking the Export Now button will download a current worksheet with all the site users listed.
The Excel worksheet that is downloaded has a column for the passwords for the users on that site. If the password column is blank, then no changes to the passwords happen when updating the worksheet back to the site. If the password column does contain a value, then the password for that user will be reset on the site to the new value.