Do I need to open Nahimic App and let it open in order to get Nahimic audio effects working?

No you do not need to open Nahimic interface to enjoy Nahimic audio effects. Nahimic audio processing will work automatically in the background. If you want to turn OFF Nahimic effects you simply have to open Nahimic app and switch OFF the global ON/OFF button in the Audio tab (same for Microphone). 

You can basically control all Nahimic effects (ON/OFF buttons) from the interface, when you close or minimize it, the processing will keep working until it's ON.

Note: you might feel the audio effects changing when you close/minimize the app while using Smart profile. This is a normal behavior because of the way Smart profile is working based on application detection, among other things.