This isn't a limitation of VoiceAttack so much as it is a limitation of Windows. As the graphical user interface is designed, as the name implies, to interface with users, not programs, a window must be visible to interact with it when using input methods designed for human interfacing.
In other words, no, it is not possible. Unless the game offers an alternate method for input, VoiceAttack can only interact with it like a human would.
Even if you had a second monitor, any time VoiceAttack needs to interact with an application, that application will gain focus, meaning that while VoiceAttack is sending input to one application, you cannot send it to another.