Generally speaking, You cannot add a ArcGIS toolbox to QGIS, as they rely on Arcgis to work.
Most of the python scripts, actually call the standard ArcGIS Geoprocessing tools. Very Few Scripts are pure Python, or call other libraries.
Since there is no 1:1 correspondence between ArcGIS geoprocessing Tools and QGIS's pyqgis, you really can't expect the scripts to work without modification.
Coming to toolboxes. ArcGIS's .tbx files are binary files in a proprietary format, and cannot be read outside of ArcGIS.
Hence, generally speaking, you cannot add and use an ArcToolbox with QGIS.