Hello there! I'm glad to help you today!
Unfortunately, no. You will need a separate microphone to both use high quality audio, and microphone use. Or you will have to stick to low quality audio+microphone by enabling hands-free mode.
Bluetooth headsets can only use one mode at a time, which is why you get good sound or a working mic, but not both together.
Unless your Bluetooth headset have a dedicated dongle that can enable both at the same time.