I don't think we do know. If I had to guess I'd say it wouldn't, since Crowley seems immune to Rowena's magic and devil's trap bullets aren't much more than an annoyance. And somewhere, I can't remember where, I think we learned that Ruby's knife couldn't finish him, either.
I don't think that Ruby's knife could kill Crowley if it couldn't kill Abaddon. You would think that their powers would be at least equal, or he more powerful than her (he's the King, she's a Knight).
The fact that he smoked out of his body before Cas could stab him with an angel knife kind of answers that question. No point in running if the knife can't kill him. :)
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