It might, but it might not. GFCI's work on a very simple premise. They compare the current flowing through the hot leg with the amount of current flowing in the neutral. If the currents don't match, the unit trips as this implies some current must be flowing to ground. (It's a Kirchoff's current law thing) If you have a short between the hot and neutral a GFCI will not trip. If you have a short between the hot and ground it will trip. A GFCI will not trip to protect you from a high resistance connection or an overload. Remember, your outlet is only rated to 15 amps and your power strip may be rated to less than that. Odds are you have a 20 amp breaker feeding it. This means your power strip can start a fire if you are running 18 amps through it and your breaker may not trip. I can't stress how important it is to know how much load you put on a circuit. If you can't measure it, all electrical components should have a Watt rating listed. Your 15 amp outlet is rated for 1800 Watts. Take the time to do the math to ensure that if everything you have plugged in would turn on at once that you wouldn't exceed this rating. One more important thought on GFCI's. GFCI Outlets should be tested monthly!!! They put that test and reset button on there for a reason. It is not at all uncommon for a GFCI outlet to fail. Newer GFCI's are designed to fail off however older designs would fail energized. Lightning strikes and power surges can easily destroy a GFCI outlets sensing circuit. I've only had 1 go bad on my 10 year old home but my brother has an older house and over half of his didn't work when I checked them while visiting.