That's a good question. My first guess is to say "no" because if you run two independent instances of the trajectory generator, they should run in their own memory spaces without impacting each other.
Are you using multiple instances of the trajectory generator?
Could you run some tests where you 1.) run multiple single axis starts in a loop with variable loop rate to find out if you are really facing the timing issue that I have mentioned and 2.) a similar test but with 2 axes that are started sequentially (again with variable timing)?
To prevent damage you should check in your control loop if the difference of the position setpoints in subsequent iterations is within a reasonable limit and stop the axes if not.
