Will Immerse Gamepack FFXIV app work together with other Immerse Gaming software?

No, it wouldn't work with any other Immerse Gaming software. Immerse Gamepack app works only with the Final Fantasy XIV edition game, and you can pick any headset you have, whereas other Immerse Gaming products are compatible with listed headsets and their model only, and it works well in any game you play with the supported headsets.  

Also, Immerse Gamepack is 360 audio rendered INSIDE the game, whereas the Immerse Gaming software relies on a surround sound output from your game.