Yes, you can lower a1c through cutting carbs. And there are other ways that can lower a1c:
First you can eat whole foods. You have to cut out the processed and packaged foods because most of it is just junk. Eat as natural as you can, and eat whole foods that come directly from nature. This is very important because it not only reduces blood sugar levels and a1c, but works on the inflammation and metabolic problems that you have as well. So the result is way better than just trying to reduce carbs.
Then you can eat more vegetables. The key is to eat more vegetables, particularly the type of vegetables that grow above the ground, such as cucumber, lettuce, spinach, zucchini, tomato, green beans, brussels sprout, cabbage, asian greens. Vegetables contain many minerals, vitamins, polyphenols, and compounds that help nourish the body and lower blood sugar, a1c and inflammation.