Yes it does. Don’t go working away, for instance, putting you `/etc` directory in git and then switching branches.
Git may change your directories to `755` and your files to `644` which will cause the system problems with security, and may even prevent booting.
look at etckeeper or this tutorial for more information about keeping `/etc` in a git repo, but the answer to “Does Git change file permissions?” is a definitive “Yes”