Howdy!
Bluetooth headsets may not work with this game it depends very heavily on the headset itself we have a pinned post at the top that might help: Voice Chat issues with Bluetooth Headsets - Technical Support - SC2 Forums (blizzard.com)
If the headset comes with a USB dongle for wireless non bluetooth and you run into issues you may consider consulting with the headset manufacturer for details on troubleshooting this issue. If they report back any useful information, posting that here for others to find is always helpful!
Thank you.
Thank you.