Making juice out of an actual grape fruit, is it as good and beneficial as eating the grape fruit first thing in the morning?

Fruit is better . To eat the fruit itself is probably more nutritious and will have more fiber. If you add sugar to the juice the calories will increase. Be aware that grapefruit juice interacts with some medications elevating their level in the blood and can be very toxic. Somehow grapefruit helps to decrease weight.
The real thing. Eating the real thing is always better than drinking its juice. Although grapefruit may not feel like it has much fiber, it certainly has more than juice. That will help you absorb the nutrients better by slowing down the digestion even a little bit.