Not natively, no. That type of functionality would go against the EULA/ToS for just about all online games.
The developers of certain games may choose to offer methods to retrieve specific information on ingame states, E.G. Elite:Dangerous has a "journal" file.
Getting that information into VoiceAttack would normally be done using a plugin (for Elite:Dangerous specifically I believe there are a few out there, E.G. the third-party "EDDI" application I believe has one).