Yes, as long as your headset’s microphone is connected to your computer, you can use Tali’s voice functionalities. Also, note that it doesn't need to be a sophisticated device -- the microphone you might use for a normal video conference will suffice.
Setting up your headset microphone
Chrome Browser
Step 1: Navigate to website you want to use Tali on e.g. https://tali.ai/install
Step 2: Click on the icon to the left of the website name
Step 3: Click on the arrow to the right of 'Microphone'
Step 4: Make sure the Microphone is allowed and the 'Allow on every visit' is checked
Test your Microphone is working - if not proceed to Step 5
Step 5: click on the box with the arrow next to 'Manage'
Step 6: Click on the button beside 'Site can ask to use your microphone'
Test your Microphone is working - if not proceed to Step 7
Step 7: Change the Drop Down box at the top to access other Microphones on your computer
Step 8: Select a different microphone and test to see if it's working