In the short term going over or driving over rumble strips should not do any damage to the tires.
But if you constantly drive over those rumble strips then eventually they could damage your tires.
But just driving over the rumble strips to pull off to the side of the road or during a time when you're about to go off the road should not do any damage to the tires.
The rumble strips however are there to save lives and they did save my life when I drifted off to sleep on a road trip one evening.
They create noise and vibration in the car or vehicle to hopefully alert the driver to the problem and hopefully they wake up before they go off the road.
The way that rumble strips make noise for the vehicle driving over them is because the tires on the vehicle drops roughly into the groove of the rumble strips.
Then as the tires roll over the rumble strips the rumble strips cause vibration and then the noise with the tires and they are meant to alert drivers that they are going off the road.
They did work for me one evening when I was driving on a road trip and I started to drift off to sleep and went over those rumble strips and I felt the vibration in the steering wheel as well as heard the noise which woke me up and I was able to pull off to the side of the road safely.
Then I drove easily and slower for about 5 more miles until I reached a town and found a motel to sleep.
So for some people those rumble strips work and save lives and it certainly did for me.