Will a patched up Zopim Chat work?
Does it mean I can use it safely on Drupal 8?


This is subject to the code written to port the module, and might be prone to some issues. The best way to find that out is by testing the patch and reporting back (on the same drupal.org thread) if you find it to be working or if you come across any issues.


  Is it ok to use patched up Drupal 7 contrib modules on Drupal 8?


Again, IMHO the best way is to work with collaboration here:


If you are a developer, help contribute the code.
If you are a tester, help with testing the solutions; and contributing to tests.
If you are good a documentation, write about the solution.
Many more ways to contribute... Check the "contributed projects" section from https://www.drupal.org/8/ready for good resources.


As per your main question:


  Will Zopim Chat work with Drupal 8?


It surely will, if those who require it help make it work!