1.Thrust reversers are normally stowed in a mechanically locked position, so that in case of a hydraulic system failure they remain closed.
2.Hydraulic pumps are mechanically driven by the engine during and after engine start. A "cut" hydraulic line would spew tremendous amounts of fluid while under pressure at 3000 psi and trigger a cockpit warning light. Hydraulics power all major aircraft systems including brakes and nose-wheel steering. I doubt Flight 587 would even have been able to taxi to the runway for takeoff had this "cut line" scenario occurred.
A friend of mine was on a Fokker F-50 that sprung a major leak on the left main landing gear. The fluid was literally gushing out as the plane was taxiing out to the runway. The flight crew had no indication in the cockpit.
I used to work on F-4J AWG-10 radar, and saw a radome full of hydraulic fluid that leaked from the antenna.