rayjimmy is absolutely correct, in my experience and humble opinion.
Acrobat password security is exceptionally weak. There are better solutions, primarily eSign PDF services that offer more robust security, such as: inability to download the file, disable printing, time-expiration, etc. Allof those features would be crucial to your app; particularly the anti-download/expiration. The worse thing that could happen is those documents remain floating around.
Technically Acrobat security can also disallow changes, printing, etc -- however, the problem being the ease of removing the password protection and that the file would continue to reside on an accessible resource, as opposed to restricting download as with the eSign services.
Off the top of my head, I can't remember whether they have batch-functionality for assigning a large number of different passwords; however, there are several businesses in this niche and ideally I hope that one would fit your need.
If you don't truly care about the most secure solution, I agree that a simple scripting language like Python with a good PDF library (eg PyPDF2) would definitely be the easiest route.