Does UnitySync synchronize passwords?

It does not, but emPass does!

UnitySync synchronizes object attribute information (e-mail, telephone number, etc). Each directory server encrypts their password field thus making it unreadable by UnitySync. Additionally, even if you schedule your syncs, they typically only occur once a day, which is too long to wait for password updates.

emPass, on the other hand, keeps passwords in sync in real-time across multiple domains.

If you need real-time password synchronization, give emPass a whirl. If you only need to set an initial password, UnitySync can, however, do that. Please see Setting Active Directory User unicode password for that solution.