Would a gyro in motion fall with more force from the same height as a nonrotating gyro of equal m?

the increase in speed increases the gyros total momentum and inertia. making horizontal acceleration akin to having an object that simply has more m. a car with spinning gyros has to fight the road more to make a turn. if it crashes into a barrier, it will less likely be stopped if the gyros were spinning sufficiently fast. but gravity isnt quite a force as it is a warping of spacetime though it can be measured exactly like a force and performs macroscopically as a force. will the increased inertia/momentum caused by its angular momentum also cause a change in projectile paths in the vertical dimension.