I got to admit I'm a bit confused now to what 'ad-hoc' refers to. My initial impression was a computer-to-computer setup, but since you mention internet on it I presume some kind of configuration or protocol is involved to point to a gateway? The Kobo is being configured by DHCP alone so you would have to work from that.
As soon a wireless connection is established, my device issues a GET request of the url I mentioned (Others have reported an apple url so it might vary.) Even when this fails, I have internet on the device briefly and this seemed very similar to the behaviour you described in the update about using your android's access point.
I don't know about mongoose. I could get by with nc (netcat) only.
You do not have to root or hack the device if you have control over the network node it connects to. But neither that or hacking the device are trivial solutions in my opinion. If you want to learn, getting familiar with
Wireshark is a good starting point.