Is there anything that can be used to verify cookie clicker runs on iPad? Would just being able to hear me tapping the screen be enough?

yeah if the sound is clear enough that's fine.

is touch screen allowed?

only under fast click

it's allowed in left click if you can only click once at the time with your finger, but if you can like click with 2 fingers at the same time and the touchscreen registers 2 clicks then it's fast click. Depends on the device.