This is a slightly futzy area still, as I don't think GW has cleaned up the language. That said, here is my understanding;
Per the rules for gun emplacements - you fire it 'instead of their weapon'
Per MCs - they can fire 'up to two of their weapons'
So, to use the emplacement, you cannot use 'their' weapons.
To fire two weapons, they have to be 'their' weapons.
So you may either use the emplacement or their weapon, but not both.
Even if, somehow, it gets to the stage where that does work, it still wouldn't work for the Avatar because he only has one shooting attack to use instead of - so he'd still need to sacrifice it to use the emplacement.