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A warrant would appear on any background check. As a result, whether you can travel internationally depends on whether you will be stopped and subjected to a random check either entering or leaving the country. If it does come up, you will be detained and arrested and held for extradition.
No. Random checks occur by pulling an occasional person aside for a check. Customs performs more of these checks when reentering the country than in departing.
No. I cannot. It is random and varies by day and by country you are reentering from.