Retainers are permitted if your orthodontist verifies that treatment is complete. But you have a problem. You lied to the MEPS by withholding pertinent medical information. You signed a statement attesting that you did not lie or withhold information and acknowledging that doing so is a felony. You lied anyway -- for something that wasn't a DQ to begin with.
The upside is that it is unlikely to be a problem. The downside is that it *CAN* be if someone wants to make it a problem. You are presently DQ for service for fraudulent enlistment. If someone comes across that in your record and they decide to make it an issue, well, you're sunk. You lied on official government paperwork that told you it was a felony to lie or withhold information. You can be discharged just for that -- it doesn't ever have to cause a medical problem. If you are in line for a T/S clearance, that can sink that too. The military does not give you a second chance to lie to them. You already proved you'll lie when you think it is to your advantage. That makes you a bad security bet.
So in short: Yes, you can bring it. No one will throw it out. But if they want to kick you out of the military, they have the grounds to do so already. That's not likely, but it's still on the list of possibilities.