Is it safe to use the mobile headset on the PC

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.