It probably would have failed.

The Gulf War Patriot was designed to shoot down Mach 2 jets, not Mach 5 Scuds.

Detonating slightly late against an aircraft is actually a good thing, since it makes the Patriot explode near the aircraft's middle instead of its nose.

A Scud is a short range ballistic missile. Once it's burnt out its fuel, it just carries on under the influence of gravity. From that point on, the only important part is the warhead in the very tip of the nose.

Detonating by the mid section of a Scud means you're just shredding empty fuel tanks. And the huge speeds involved might actually make Gulf War Patriot missiles detonate against the rear of the Scud and just shred the non-functioning engine, or even detonate behind the Scud entirely.