What you're describing is how "listening" works already: The speech recognition engine keeps running in the background as normal, VoiceAttack just ignores any recognized commands.
If you have a "Make VoiceAttack Start Listening" action at the top of any command, that command will still be executed if it is recognized while listening is disabled.
You can also use the "Override listening if my spoken command begins with" option on the "Profile General" tab of the profile options window to set up keyword(s) that work as a prefix to execute commands while listening is disabled.
E.G. if you have a command with the phrase "do something", and you have "computer" set as an "Override listening if my spoken command begins with" phrase, you can say "computer, do something", and that command will be executed regardless of listening state.
More information can be found in the manual, VoiceAttackHelp.pdf, which can be opened by pressing F1 while VoiceAttack has focus.