The Kobo's
processor supports acting as a USB Host (or
OTG host), so with a new kernel (or at least a module) and a small hardware hack, it seem possible to me. I don't have a Mini and I haven't traced the circuit on my Glo but I suspect you'll have to modify a few PCB traces around the USB connector to get the Kobo acting as a supply for connected devices.
Some pointers:
Datasheet:
IMX50CEC.pdf
Reference Manual:
IMX50RM.pdf
System Development Guide:
IMX50SDG.pdf
If you need anything on their linux driver implementation, download IMX50_1104_LINUXDOCS_BUNDLE but you'll need
an account there.