Yes, you can translate all customer facing copying into another language. You can also translate the app into any active language on your store - if a customer checks out in that language, your overrides will be used. 

To translate customer facing copy, check  Translations under Settings.

How do we translate the post purchase header text?

Shopify inserts a mandatory header on the post purchase page and this can be edited within your admin's theme language:

Go to Online Store -> Themes -> Live theme -> Actions -> Edit languages:

Then search for: "You've paid for your order." or "View order confirmation":