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Nope.

They were thrown a thousand light years away from the planet by . On the way back they were sabotaged; the "The emergency bypass control of the matter/antimatter integrator is fused', which caused the engines to go "running wild". They solved it by using a magnetic probe to shut off the fuel flow.

So whilst it wasn't something they did themselves, all that the sabotage did was basically eliminate the safety system and so dump the maximum possible power into the warp drive - essentially exactly what the Orion would have done with his engines.

Like I said, I wasn't sure I recalled it properly. Well, there it is. I still seem to remember (I'm afraid I don't have the references to hand) various non-canon publications - RPG supplements, etc. - extrapolating a big Orion advantage in propulsion tech, but non-canon sources are necessarily non-canon.

For a race of pirates they would need it. But at the time of TOS, Starfleet only had the Connie's that could push that speed. The Orions may very well have been able to run rings around everything before.

Mmm... Orion rings...




Wait...

The melons are better

Even if I hate what Ent did to the Orions watching those three gyrate really made up for it.