look at a Galazy Class' MSD there is no warp core. It possible they forgot to include it but...ifyou look at an Intrepid class' MSD there is a secondary warp core visible.
according to memory alpha (a respectable source)
the saucer is not equipped with warp drive, only impulse engines. During a high warp separation, the stardrive section would need to slow down just long enough for the saucer, still riding the decaying warp energy, to clear. Otherwise, there would be risk of the stardrive section slamming into the rapidly slowing saucer
If the saucer is ever seen at warp i think it is an inconsistency