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No I don't think it would. The star wouldn't feel anything as it passed over the event horizon. Not until it becomes close enough to the singularity would it start to become stretched and break apart. However, if it was in abort around the black hole the tidal forces it might tear it apart before it even reached the event horizon, just like comet Shoemaker-Levy 9 did before it struck Jupiter (though that didn't involve a particularly large event horizon).
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