[iudqnolq]

No, creating a git commit merely requires knowing the current state of all the files and the hash of the previous commit. You don't need the actual contents of the previous commits.

https://git-scm.com/book/en/v2/Git-Internals-Git-Objects

Pushing from a shallow clone to a remote is more complex, but is supported in modern git versions.

https://stackoverflow.com/a/6900428