If you overload a circuit you most likely trip a breaker. That's not a good thing but is a safety precaution to prevent burning up anything. It shuts down the unsafe power supply and requires a walk over to reset the GFI or a breaker. A surge protector is kinda like a big catcher's mitt to prevent any overvoltage condition passing through. In my experience it doesn't shut power off but kinda acts like my turbo blow off valve, diverting the overvoltage away.
If you are tripping breakers of GFI's you need to evaluate what you can safely run on that circuit. When you exceed the draw or demand it shuts down. Either have an electrician up your rating or plug them into different outlets (circuits).
I am not an electrician so please correct me if I'm wrong on this.