For clarity, your question actually pertains to how EnergyPlus, which is the simulation engine used by OpenStudio, is handling the ground temperature, not really OpenStudio.
There is a question of how OpenStudio translates the object you are using, which has to be GroundHeatExchangerVertical, is actually translated to the related EnergyPlus objects though.
I suggest your look at the resulting in.idf that OpenStudio generates during ForwardTranslation, in the model companion folder. (so if your model file is model.osm, look next to it into model/run/in.idf to inspect it), but I will give you the lay of land anyways.
Your OpenStudio GroundHeatExchangerVertical will be translated into (links point to the E+ 9.5 Input/Output Reference)
(Note: the reason it differs between OpenStudio and E+ is that this object was added to OpenStudio a long time ago, and at that point EnergyPlus had this structure. The refactor with the introduction of the new GroundHeatExchanger:System was done in E+ 8.9)
The Source for the ForwardTranslator method for this object can be found in ForwardTranslateGroundHeatExchangerVertical.cpp, and that is the definitive source of which fields map to the various E+ objects.
Anyways, the key point is the Site:GroundTemperature:Undisturbed:KusudaAchenbach object, which is used to calculate the ground temperatures at varying depth. The model and its equation is described in the Engineering reference here. How these fields are populated can be easily read ForwardTranslateGroundHeatExchangerVertical.cpp#L193-L214
The OpenStudioGroundHeatExchangerVertical'sGround Thermal Conductivityfield is mapped to E+Soil Thermal Conductivity`. - The OpenStudio GroundHeatExchangerVertical
Ground Temperature field is mapped to the E+ Average Annual Ground Surface Temperature for example, - The E+
Average Amplitude of Annual Ground Surface Temperature and Phase Shift of Minimum Surface Temperature are defaulted to 3.2. and 8.0 respectivaly - Density and Specific Heat in E+ are derived from the OpenStudio
Ground Thermal Heat Capacity.
In summary: No, it does not take into account the EPW weather file you pass in. The minimum effort to tweak the ground calculation would be the change the GroundHeatExchangerVertical Ground Temperature field. If you wanted to modify the phase shift and average amplitude, you will need an EnergyPlus measure for that. So, start changing the Ground Temperature field, and look at the impact is actually has on your results. If your borehole is going down to 100m, it might not represent a strong effect.
