Can missing cage mount screws cause the frame to rust?
It is possible for water or sweat to enter the frame, and for corrosion to build up. Any rust would be most likely to happen on the steel bolt (which is missing) rather than on the aluminum frame, but oxidization comes in many forms.

While this is unlikely to cause you any significant issues, it's an easy fix. Any M4 threaded allen bolt, between 1.5 and 2.5cm will fit just fine.

Stop by the hardware store or your LBS, and you'll be sorted in just a few minutes.