No, that’s not related to this plugin’s function.
This plugin can only cause the menu to run the map or battle scene in the background, and provides an optional alternative pause function to make up for that. In the case of battle scenes, any plugin that allows opening another scene in battle must also make the battle scene resumable (which isn’t trivial, so it’s rarely done. Battle Core VisuStella MZ has this feature I believe, but it’s implemented in a way that causes bad glitches when combined with my plugin here. I’d hook it to provide better support for the combination, but can’t do so due to the obfuscation there).
The most compatible way to implement this would be to add the necessary Window_s and logic directly to the Scene_Battle, but I’m not aware of any plugins that do this.