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Yes it will still crank it just wont fire and run.
I would not recommend it, as sensitive circuits in the PCM could be damaged.
It could be a number of things, but experience tells me it is most likely either the bad Pcm diode or it could be a faulty camshaft sensor or as simple as a bad glowplug relay. Is there any smoke from the exhaust when you are cranking it over?
I will be away for the rest of the day, but will be back online around 7:00 pm.