Will it damage my audio chip or corrupt any driver?
No and no. Assuming you're talking about passive headphones + mic with TRRS connector, there's no way it should damage your audio chip, and it is (almost) totally driver-independent.
It's quite likely that you can plug your headset into your PC/Laptop and use the inbuilt headphones without any problem. Many recent 3.5mm TRRS jacks have been constructed to be compatible with stereo headphone (TRS) sockets)
Note that you will not be able to use the Mic in your headset when doing this. To make use of the headphones AND the mic you'll need an adaptor to go from
TRRS (mic+stereo) --> TRS (stereo) + TRS (mic)
From the wiki:
A three- or four-conductor version of
the 2.5 mm plug is widely used on cell
phone handsfree headsets, providing
mono (three conductor) or stereo (four
conductor) sound and a microphone
input. Common stereo headphones with
the 2.5 mm plug are often not
compatible with this type of socket. A
3.5 mm version of this plug is now commonly available on mobile
telephones as well. A 3.5 mm
stereo-plus-mic jack is available that
is compatible with standard 3.5 mm
stereo headphones, e.g. Nokia has been
widely using TRRS connectors with 3.5
mm diameter since 2006. The selected
pin assignment, with ground on the
sleeve, is as well standardized in
OMTP and has been accepted as a
national Chinese standard YDT
1885-2009.
TRRS plugs do not work properly with a
TRS stereo jack if the ground contact
in the jack connects to the microphone
contact on the plug. It is therefore a
good practice to implement new TRS
headphone jacks using actually a TRRS
mechanical jacks and connecting ground
to sleeve as well as the second ring
contact. This way such jacks will
provide better compatibility with
different TRRS cell phone headsets.