No, but consider what you need to know about file systems to use them. At the barest minimum, you need to know that:
* Data is stored in files
* Files have names
* Files are contained in directories
* Directories have names
* Directories can contain directories
If you had no understanding of what a file or a directory was, I'd imagine you'd find the behaviour of "grep" or "cat" completely unintuitive.
You don't need to know how Git stores data internally, but you do need to have a basic understanding of its design, just as you need a basic understanding of a filesystem in order to use it.