Does It Use WebClient

No. Zee Drive does not use the Microsoft Windows WebClient Service (AKA WebDAV). Zee Drive is a separate technology to the Windows WebClient service.

Whilst the WebClient service is commonly referred to as WebDAV, it is not in fact WebDAV. WebDAV is a communications protocol. The WebClient service uses WebDAV to communicate with SharePoint. This is an important distinction.

WebDAV is not in itself inherently slow as it is a protocol. Slowness would be an artifact of the implementation either of the WebDAV client or WebDAV server, or both.