The VEX rules for modifying your robot are as such:
<R1> Only one (1) robot will be allowed to compete per team in the VEX Robotics Competition. Though it is expected that teams will make changes to their robot at the competition, a team is limited to only one (1) robot. The VEX Robotics Design System is intended to be a mobile robotics design platform. As such, a VEX robot, for the purposes of the VRC, has the following subsystems:
Subsystem 1: Mobile robotic base including wheels, tracks, legs, or any other mechanism that allows the robot to navigate the majority of the flat playing field surface.
Subsystem 2: Power and control system that includes a VEX legal battery, a VEX control system, and associated motors for the mobile robotic base.
Subsystem 3: Additional mechanisms (and associated motors) that allow manipulation of game objects or navigation of field obstacles.
Given the above definitions, a minimum robot for use in any VRC event (including skills challenges) must consist of 1 and 2 above. Thus if you are swapping out an entire subsystem of either item 1 or 2, you have now created a second robot and are no longer legal.
a. Teams may not compete with one robot, while a second is being modified or assembled.
b. Teams may not switch back and forth between multiple robots during a competition.
Under these rules, would it be legal to change the drive gear ratio of a robot?