We ran the gyro through the Sensor Mux before and did not have any issue with it. The only issue is that from time to time, the students may forget to turn the power of the sensor mux on and did not realize it until autonomous failed miserably.
A lot of RobotC functions are not thread-safe. In fact, I recall reading some posts about RobotC doesn't support calling a function from different tasks. Even if RobotC supports calling a function from different tasks, you still need to determine if the function is written such that it is thread-safe (e.g. no accessing global resources etc). I assume you are calling Xander's Gyro driver? If so, Xander can comment on if his Gyro driver is thread-safe.
A lot of students don't understand how to do multi-tasking programming properly anyway. That's why we have been avoiding RobotC tasks altogether. We do our own "cooperative multi-tasking" which is a lot safer and don't have all the gotcha's of preemptive multi-tasking.