I could be wrong, but I don't think a bad booster would cause the pedal to go to the floor as the whole point of the booster is to give you vacuum assist to apply more pressure to the brakes than you can do just with your foot. If anything a bad booster would cause the pedal to feel more stiff and give you worse braking performance.
Not sure what year your Edge is, but you might look up the issue with the ABS module and sticking plungers in the HCU. This issue is caused by using DOT3 brake fluid (which *was* recommended by Ford) and it being incompatible with the metal used inside the HCU causing the valves to stick. When a valve sticks open, it allows the fluid to circulate around inside the HCU rather than applying it to the calipers/brake pads which causes the pedal to go to the floor. I'm currently dealing with this exact issue on my wife's '13 Edge Sport. I just ordered a new HCU from Ford to the tune of $680... even though I feel like Ford should be covering this part due to their own poor choice in recommending an incompatible fluid. Maybe they can also cover the updated valve cover that I also just purchased and replaced due to the faulty original design that allowed massive amounts of engine oil to get sucked into the intake (the 'accordion' ribs on the intake boot were completely full of oil along with the throttle body) which burned out the rear catalytic converter.