HearthSpeak is a program that allows you to control Hearthstone through voice commands.
Download the latest release here. Save HearthSpeak.exe anywhere and run it.
You can also clone this respository and compile the source code in Visual Studio.
Be sure that your microphone/recording device is ready before running HearthSpeak. The first time you run Hearthspeak, Hearthstone will need to be closed or restarted to properly sync the log file.
Click here for a list of available commands.
According to this tweet, the answer appears to be yes. HearthSpeak converts speech into clicks and keystrokes however, so some caution regarding its use might be a good idea.