No, they probably won't let you wear them at basic. TRADOC can be AR about those things. I had a SSG try to come up to me one time and tell me to take them (my M-frames) off, I just looked at him and laughed and told him that Army regs allowed me to wear them, as they were black frame with black lenses, they have a NSN, and were purchased from the PX as compatible with the Army uniform. His response was, "Well, yeah, you're right, but it's kinda taboo to do it. I just stared at him, and he just walked away. He was a duecebag anyways. But that's a different situation. In basic training, you do what the Drill Sergeant tells you too, PERIOD. Odds are they're not gonna let you wear them at all, and if you take them they will be seized and returned at the completion of the course.
What did he want you to wear instead... i mean.. which shades were issue or allowed before the M-Frames?
Sunglasses are great for keeping the sun out of your eyes. Some will protect the eyes in other ways. But we are not in a who can get the coolest shades competition, we are in the business of closing with and killing the enemy.
Sunglasses restrict peripheral vision, distort the view of what you are looking at (some to advantage, some not), shine and reflect light and obscure your eyes.
If you have a conversation with someone and you cannot see their eyes - it's downright f**king rude. It alienates people.
If you're talking to 'Haji' or whoever else, take your shades off. They may just be inclined to talk back.