It could be argued the pipes are for tapping the raw output of the warp core and safely siphoning off fractions of plasma to feed the EPS grid that runs through the neck and into the saucer, but that still leaves the question "where is the warp core?" If we take the set diagram at its word then the intermix chamber (basically the core of the warp core cause its where the boomboom happens) is that modest black pillar full of salt crystals in the middle of the set and this is reinforced by broken circle where Michelle(?) messes with this pillar's console to fake a warp core breach, BUT in both "ghosts of illyria" and "those old scientists" the attention of the characters and the viewer is instead directed at the glowing spot on the far wall of the cathedral when admiring/messing with the warpcore, but according to the set diagram that's just the back side of the deflector dish...
I think we agree that one positive we can say about all this is SNW is going above and beyond being true to TOS by being not only vague, but inconsistent.