Never a bad thing to have a surge suppressor especially on a small source like a generator. I’ve seen a number of generators over the years fail and go to full field producing 2 or 3 times rated voltage if voltage regulator loses sensing.
The suppressor will help protect your loads and will likely trip the generator circuit breaker in the above situation. It does not protect the generator.
Like many types of insurance you will probably never know if you needed it if it did its job well.