Can a diabetic can drink a protein shake?

Yes: No reason a diabetic shouldn't drink protein shakes. If you have other comorbidities that may compromise your ability to process protein, then this may play a role.

Yes, but no: You can, but you don't want to. All protein drinks are is a bottle of extra calories -- calories that you probably don't need and don't want. Try 3 meals during the day, it's cheaper, tastes better and is much better for you. Protein shakes are metabolized to calories, just like anything else - otherwise you'd end up looking like what you eat.