Yeah, you can run web management for a Tea*Speak server outside of the Tea*Speak client.
You need a web panel that talks to Tea*Speak ServerQuery API. There are a few out there that let you manage users/channels/permissions through a browser.
If your server runs on a VPS, you can install one of these panels. You can set it up on the same machine or a different web host. Then, connect it to your Tea*Speak ServerQuery. This way, others can access it without using the Tea*Speak client.