During a Time Capsule 35 Pass Erase, do I have to keep my computer on / running?

Back Story:

Okay, so I just upgrade my Time Capsule from a 2 TB (802.11n) to a 3 TB (802.11ac). Yay! However, after transferring over all my files, I needed to erase my old Time Capsule Partition.

I chose the 35 Pass Erase, because of the extremely sensitive data on this back up. (not really, but I just want to be safe).

Question:

So I started the erase! But I need to know if I turn off my computer, will the Time Capsule continue erasing on its own? Or if I loose my internet connection, will the Time Capsule keep erasing?

I really prefer not to have my computer on for that long, and I need to take my computer to work tomorrow...

Other Notes:

I am connected to my Time Capsule throughout Ethernet, and have WiFi disabled.

The The Time capsule doesn't need your Mac to run. Once it receives the wipe command, it will run to completion without needing anything but power from the all. (Ok - you could cancel the erase or it could error out, but in most cases the erase completes on its own accord.) You also don't need a Mac to start the wipe command. Airport Utility runs on Windows and iOS as well.