Not as bad as if the ship's orientation suddenly shifts immediately after the core's fired and it impacts the saucer. :P
That wouldn't matter since gravity flows in the direction of the gravity plates and even without direct power, gravity plates in ST will run for quite a few hours on there own.
But the ships gravity doesn't extend beyond the hull. If the core were being ejected and the ship started, for whatever reason, tumbling nacelles over saucer wouldn't the saucer be in danger of being hit?
One of the reasons I asked about a horizontal core would be that the hatch would basically be a slide that directs the core down (from the POV of the ship) and away. Old technology could be used to help speed the core on its way, a spring. Or the just nearly as old directed explosives.