yes IF it is a CDP. And many small AC adapters are for 500 ma max. Draw too much and the voltage drop can cause an overheat and failure in the charging circuit in the device or in the adapter or both.
first you determine the maximum out put of the usb port whether wall
mounted or not.the port will not deliver more than that output. its
regulated not to do so but it will happily out put current at its maximum
rate. if the load does not require the maximum current out put it will
deliver a lower current.current draw is determined by the load.
if the device plugged into the usb port requires more current than
the port is regulated at one of two things will happen.
the device wont turn on.hence no current or the device
will operate a a reduced capacity.
as for the batteries most batteries by design can handle
a higher charging current than what is delivered by the
standard charger that accompanies them.
in the case of using usb ports for operating or charging a device
the original spec was 500 ma so most devices are designed of that
spec.now as the spec goes up increasing the amount of current
available devices will be designed that can utilize the additional power.
the old devices will work fine. as for so called super charging its
just semantics as the batteries are already spec'ed to handle
that much current.they just charge faster. its similar to a bass boost
button on audio equipment,its not boosting the bass. it stops filtering
out the bass that was already there.

regards
mike