Not for long they wouldn't.
Within the atmosphere they would be subject to air resistance. Air resistance means drag, and drag means that, in the absence of some force to maintain its momentum (do your moons have giant rockets with unlimited fuel?), the moon will lose speed. Less speed means it can't maintain its orbit, so it falls lower, where the atmosphere is more dense, where there's more drag, so it slows down ever further...
You can see where this is going.
In spaceflight this is called "aerobraking"; in the absence of flight control surfaces, parachutes, air bags, or similar means of controlling one's descent or cushioning one's impact, the inevitable conclusion is "catastrophic lithobraking".