You are correct, the column would also contain the transporter circuitry as well since the engines seem to be also tied to the transporter's "velocity balancing". I think normally it is run through the main circuit but in that episode they were able to later bypass and tie it to the impulse engines so I would imagine that all the circuits are interconnected in someway.
One thing I'm curious about now is upon viewing TMP/TWOK's engine room and the vertical/horizontal energy conduits is trying to figure out where "other circuits" connect to it? We see at the bottom of the vertical conduit what looks like the reactor. We don't really see what is at the top but assume it is thing for the impulse engine. The horizontal piece runs to the back to the warp nacelles. But we don't really see any pipes/wires/etc lead off it to connect to other stuff in the engineering section.
So I'm a bit perplexed as to how that works unless the wires are inside the column supports for the horizontal conduit. Or leads come off the reactor at the bottom and we can't see that machinery. Hmmmm...