There is nothing to stop you giving birth naturally.
How has your control been throughout the pregnancy and the last few months prior to conception?
It is likely that you will be on a sliding scale of insulin during established labour, which can make it a little trickier to be mobile, it is also likely that once in established labour they will want you to be monitored with a CTG, which is where they place a couple of discs on your tummy, one to monitor the baby's heartbeat, the other to monitor the activity of your uterus.
In some hospitals, they may encourage you to get on the bed as this is deemed to be 'easier' to monitor you and your baby BUT there is no reason why you cannot be standing, sitting on a ball, on all fours on the floor, walking as far as the machine allows etc. The more active and upright you are and the more in control you feel of your own labour, then your chances of a natural birth are increased.
Concentrate now on keeping excellent glucose levels, and if you are struggling keep asking for help.
As long as you are healthy and your baby is healthy, the chances of a natural labour should be no different to that of a non-diabetic mother.
Keep positive, your body was made to birth babies, it bloody hurts, no point denying that, but once your baby is born, the pain stops, and what a reward you get!!
Good luck!!
(I am a final year student midwife, NOT qualified. The best person you can speak to is your own midwife, write down everything you are concerned about and all your wishes and take it to your midwife. If the answer is not what you want, ask why. And finally, it is your baby, your pregnancy, your labour and your choice!)