Yes. In fact, some moms find that breastfeeding can help them better manage their diabetes postpartum, since they return to their pre-pregnant state more gradually. Plus, breastfeeding reduces baby's chance of becoming diabetic in the future. There are special challenges for a breastfeeding mother with diabetes, so be sure to educate yourself as much as possible before baby arrives so you can nip any issues in the bud.
Sometimes, the babies of diabetic moms are kept in a hospital nursery for observation for a few days following birth, which can make it tough to nurse frequently at the beginning.
Talk to your medical staff and ask if you can avoid formula supplements and keep baby nearby so that you can nurse often. Let them know breastfeeding is important to you and request help from a lactation consultant if you have any questions or are having any trouble with baby's latch. If baby must be supplemented with glucose water (or anything else) ask that the nurses avoid using a bottle. (They can use a cup, syringe or eyedropper). And, if you aren't able to breastfeed every two to three hours, request a pump so that you can begin to stimulate milk production.
In the first week or so after delivery, your insulin and dietary needs might fluctuate, but you will soon settle into a routine and will learn what your body needs. Many (but not all) women find that they need less insulin during breastfeeding. (Your insulin shots won't affect baby.) When baby hits a growth spurt and feeds more often, you might need to adjust your diet/insulin a little. You'll need to pay special attention to your body and make adjustments when baby weans. (Diabetic moms do better with very gradual weaning.)
You may be more prone to mastitis and yeast infections (aka thrush) than other moms. To prevent mastitis, feed baby often and treat any plugged ducts right away.