We have personally noticed in a few cases in relatives or close friends significant reduction of carbohydrates have led to either complete non-requirement of medication to control diabetes or significant reduction in medication requirement. Diet and lifestyle changes can greatly impact the progression or development of diseases such as diabetes (and the same applies to cancer and heart disease).

There are a few relevant papers regarding low-carbs (along with high-proteins) in the diet:

Here is the first:

Frank Q. Nuttalla, Mary C. Gannon. The metabolic response to a high-protein, low-carbohydrate diet in men with type 2 diabetes mellitus. Metabolism Clinical and Experimental Volume 55, Issue 2, Pages 243-251 (February 2006)

We recently reported that in subjects with untreated type 2 diabetes mellitus, a 5-week diet of 20:30:50 carbohydrate-protein-fat ratio resulted in a dramatic decrease in 24-hour integrated glucose and total glycohemoglobin compared with a control diet of 55:15:30. Body weight, total cholesterol, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, and serum ketones were unchanged; insulin and nonesterified fatty acids were decreased. We now present data on other hormones and metabolites considered to be affected by dietary macronutrient changes. The test diet resulted in an elevated fasting plasma total insulin-like growth factor 1, but not growth hormone. Urinary aldosterone was unchanged; free cortisol was increased, although not statistically. Urinary pH and calcium were unchanged. blood pressure, creatinine clearance, serum vitamin B12, folate, homocysteine, thyroid hormones, and uric acid were unchanged. Serum creatinine was modestly increased. Plasma ±-amino nitrogen and urea nitrogen were increased. Urea production rate was increased such that a new steady state was present. The calculated urea production rate accounted for 87% of protein ingested on the control diet, but only 67% on the test diet, suggesting net nitrogen retention on the latter. The lack of negative effects, improved glucose control, and a positive nitrogen balance suggest beneficial effects for subjects with type 2 diabetes mellitus at risk for loss of lean body mass.

And another:

Eric C Westman, William S Yancy Jr., John C Mavropoulos, Megan Marquart, and Jennifer R McDuffie. The effect of a low-carbohydrate, ketogenic diet versus a low-glycemic index diet on glycemic control in type 2 diabetes mellitus. Nutrition & metabolism 2008, 5:36 (19 December 2008).

From the abstract:

Objective

Dietary carbohydrate is the major determinant of postprandial glucose levels, and several clinical studies have shown that low-carbohydrate diets improve glycemic control. In this study, we tested the hypothesis that a diet lower in carbohydrate would lead to greater improvement in glycemic control over a 24-week period in patients with obesity and type 2 diabetes mellitus. Research design and methods: Eighty-four community volunteers with obesity and type 2 diabetes were randomized to either a low-carbohydrate, ketogenic diet (<20 g of carbohydrate daily; LCKD) or a low-glycemic, reduced-calorie diet (500 kcal/day deficit from weight maintenance diet; LGID). Both groups received group meetings, nutritional supplementation, and an exercise recommendation. The main outcome was glycemic control, measured by hemoglobin A1c.

Results

Forty-nine (58.3%) participants completed the study. Both interventions led to improvements in hemoglobin A1c, fasting glucose, fasting insulin, and weight loss. The LCKD group had greater improvements in hemoglobin A1c (-1.5% vs. -0.5%, p=0.03), body weight (-11.1 kg vs. -6.9 kg, p=0.008), and high density lipoprotein cholesterol (+5.6 mg/dL vs. 0 mg/dL, p<0.001) compared to the LGID group. diabetes medications were reduced or eliminated in 95.2% of LCKD vs. 62% of LGID participants (p<0.01).

Conclusions

Dietary modification led to improvements in glycemic control and medication reduction/elimination in motivated volunteers with type 2 diabetes. The diet lower in carbohydrate led to greater improvements in glycemic control, and more frequent medication reduction/elimination than the low glycemic index diet. Lifestyle modification using low carbohydrate interventions is effective for improving and reversing type 2 diabetes.

They also state in their 30 page paper, in the discussion:

In this study, both a low glycemic index, reduced-calorie diet and a low-carbohydrate, ketogenic diet led to improvement in glycemic control, diabetic medication elimination/reduction, and weight loss in adherent overweight and obese individuals with type 2 diabetes over a 24-week period. The diet containing fewer carbohydrates, the LCKD, was most effective for improving glycemic control. In patients taking insulin, the effects were often quite powerful. For example, participants taking from 40 to 90 units of insulin before the study were able to eliminate their insulin use, while also improving glycemic control. Because this effect occurs immediately upon implementing the dietary changes, individuals with type 2 diabetes who are unable to adjust their own medication or self-monitor their blood glucose should not make these dietary changes unless under close medical supervision.

The underlying principle of carbohydrate-restriction and the historic precedents of using the low-carbohydrate diet for type 2 diabetes suggest that the low-carbohydrate approach may be one of the most effective dietary treatments for diabetes.

And in the conclusion:

In summary, lifestyle modification using two diets that reduce carbohydrate intake led to improvement in glycemic control, diabetic medication elimination/reduction, and weight loss in overweight and obese individuals with type 2 diabetes over a 24-week period in the outpatient setting. The diet containing fewer carbohydrates, the lowcarbohydrate, ketogenic diet, was more effective for improving glycemic control than the low glycemic diet. Lifestyle modification using low-carbohydrate diet interventions are effective for improving obesity and type 2 diabetes, and may play an important role in reversing the current epidemic of 'diabesity.'

Some other quotes from the authors of the study in reporting coverage:

Patients who followed the no-glycemic diet experienced more frequent reductions, and in some cases elimination, of their need for medication to control type 2 diabetes, according to lead author Eric Westman, MD, director of Duke's Lifestyle medicine Program.

"Low glycemic diets are good, but our work shows a no-glycemic diet is even better at improving blood sugar control," he says. "We found you can get a three-fold improvement in type 2 diabetes as evidenced by a standard test of the amount of sugar in the blood. That's an important distinction because as a physician who is faced with the choice of drugs or diet, I want a strong diet that's shown to improve type 2 diabetes and minimize medication use."

And also:

"It's simple," says Westman. "If you cut out the carbohydrates, your blood sugar goes down, and you lose weight which lowers your blood sugar even further. It's a one-two punch."

The diet is not easy for everybody. "This is a therapeutic diet for people who are sick," says Westman. "These lifestyle approaches all have an intensive behavioral component. In our program, people come in every two weeks to get reinforcements and reminders. We've treated hundreds of patients this way now at Duke and what we see clinically and in our research shows that it works."