The reason to work the core is 1) to increase your core strength, naturally, but is important to note because it increases the body's ability to do nearly any activity and 2) form the muscle groups for appearance.
However, in order for 2) to be show up, the fat in that area must be minimal enough to show the muscle. No amount of core workout will show the muscle definition, and definition in itself does not occupy enough space to make a visible difference (to generalise, it is normally the opposite).
They are not bad excersizes, but they will do little to nothing for physical appearance. The only relationship would be an extremely slight increase in calories consumed by doing those excersizes, plus the additional burn from having more muscle mass. Both are minimal at best and won't make a tangible difference.
As far as cardio, do all types of excersize, including Anaerobic and strength training. Over training in one is not a effective all around, including various risks. In the long run though, only the consumption of fat (ie: aerobic/cardio + less calorie) will be the direct way of doing it.