I have PS4 controller and wired headphones. If I connect the controller to PC/Laptop via Bluetooth, will I be able to use it as "wireless headphones" by connecting normal headphones to the controller?
Theoretically it's possible, but practically you'll need a DS4 wrapper that supports the feature.
The DS4 is a Direct Input device which means it isn't widely supported by games. In return it's more flexible than XInput devices such as the Xbox 360 controller. The DS4 wrapper I'm currently using does not support the audio features of the DS4, however it does support the touchpad which emulates a mouse, and motion input which I couldn't test due to lack of software support. It also supports the lightbar and can be configured to change color depending on the DS4's batery state when connected over bluetooth.
So essentially you could use your DS4 as wireless headphone, but you'll need to find the software that supports it or write it yourself.