Does driving an microcontroller's GPIO when it is powered off weaken the chip?
Unless the datasheet and associated documentation specify otherwise, do not apply a non-ground voltage to an unpowered device. The device may become powered through the input protection diodes on the pin and could behave erratically.

If there is no way to modify the schematic such that unpowered devices do not have voltage applied to their inputs then use tri-state buffers such as the 74HC125 or 74HC244 to hi-Z the inputs when power is not applied to the device.