No, you cannot send replies to customer queries from the Cases module by default. However, you can create a custom email field for the Cases module and create a custom button to trigger the email.
Here's how you can create a Custom button in the Cases module for sending emails
1. Click on Setup > Customization > Modules.
2. Select Cases > Create Your Button > Links and Buttons.
3. Specify the button name and select View Page.
4. Invoke a URL, copy and paste it in the Construct your URL section.
5. In the Construct your URL section, choose the profiles where you would like to see the buttons.