Answer
Yes. No.
Work Step by Step
Imagine a Gaussian surface set up just outside the conductor. If a charge is added inside the cavity, this changes the charge enclosed inside the Gaussian surface, which changes the electric field strength on its surface.
The electric field inside the material of the conductor is zero under electrostatic conditions, regardless of how much charge is placed outside of the conductor. Adding more charge outside will change the amount of induced charge on the surface of the conductor, but the electric field inside the cavity will still be zero.
