Git is able to store permission bits along with files, and checking out those files will save them with the same permissions as those with which they were commited.
New repository "gitPermissionsTest" created and cloned, create two empty .sh files, set one of them as executable, the other as non-executable, add & commit & push. Delete the repo locally. Re-clone from remote repository, and attempt to run each file.
The file that was initially set as executable was able to execute, the file that was initially set as non-executable was not able to execute. Hypothesis confirmed.