Negative effects of using underrated chargers
You seem to be confusing two things, operating the device and charging a internal battery.

However, in either case using a power supply with a order of magnitude less current capability is very unlikely to work.  The device will try to draw more than the little current the power supply can produce, which will either collapse its output voltage, cause the supply to go into current limit mode if it has such a thing, or perhaps cause it to actively shut down.  Either way, the output voltage won't be 9V or anything close, so the device won't work.

Lower voltage is unlikely to damage most devices even if they don't operate correctly.  Obviously the device must be able to deal with brownout for at least some small time since no power supply can go instantly from 0 to full output voltage.