**Kiddush/chillul Hashem taken to mean showing the world that this is how Hashem's chosen people behaves:**

No, by definition: The gentile cannot be representative of a group he does not belong to.

**Kiddush/chillul Hashem taken to mean letting one self be killed rather than doing something for which one is required to let oneself be killed rather than doing:**

Yes, by definition (at least theoretically): If that is the label of an act, and he did that act, then it has that label.* (However, as per [Sanhedrin 74b][1], there may not be any actions requiring a gentile to sacrifice his life, rendering occurrence impossible.)

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<sup>* My head spins from reading my own words!</sup>


  [1]: http://hebrewbooks.org/shas.aspx?mesechta=24&daf=74b&format=pdf