For further reference, since I couldn't find any good explanations how to convert the internal value to project units and vice versa, I found this way through the Revit API:
gp_type = GlobalParameter.GetDefinition().UnitType
display_units = doc.GetUnits().GetFormatOptions(gp_type).DisplayUnits
gp_type returns the UnitType of this global parameter (lenght, area, volume etc.)
display_units returns the DisplayUnitType to which Revit converts the internal value for displaying in the user interface.
Then I could use the UnitUtils class to convert between internal and project value (display_unit), irrespective of which unit the user has set in the project units dialog and which UnitType the global parameter has.