Does Drupal modify folder permissions during runtime? Does Drupal modify the permissions on folder within the sites folder? Is there an edge case where this is possible outside of install?

I've been seeing an issue where a sites folder whether it be default or blah.com is getting it's write permissions removed after loading the site.

It's not specific to one codebase, it occurs across multiple codebases (no modifications to core) and across multiple versions 6/7.

This is problematic when using git with a specific site folder as git can no longer perform checkouts and merges without the write permissions.
Yes drupal modify default folder permission during runtime, and this folder is what exactly you should add it to your .gitignore because it contains user uploaded files which have not value to keeping in repository.