Alejandro L. answered 10/13/16
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I think your question may not have been written properly because if the triple point of a substance resides below atmospheric pressure then you will never see sublimation at atmospheric pressure regardless of the temperature (e.g. water). On the other hand, substances like CO2 have their triple point above atmospheric pressure and will sublime. In any case, atmospheric pressure will be above or below the triple point for a given substance and on its own it has no effect of a phase transition, assuming you are at the right temperature to even discuss the phase transition.
Now, if instead you meant "sublimation is not affected by pressure" then the answer is false. The change in density from solid to gas is huge and as a result will depend very much on the pressure. Likewise, the change in density of a liquid evaporating into a gas is also quite large and changes in pressure affect its other physical properties. Density changes for solids and liquids, however, are small and only really high pressures can affect the properties.
I hope that help clear up your question.