Yes, Swiss organizations can participate, as can organizations from any other country. However, they are not eligible for automatic funding for the whole programme. As of 15 September 2014, Switzerland is a partly Associated Country (AC) to Horizon 2020 and can only receive funding for certain areas in the programme. These areas are:
the "Excellent Science" pillar (the 1st pillar), containing the European Research Council, Future and Emerging Technologies, Research Infrastructures and the Marie Skłodowska-Curie actions;
actions under the specific objective “Spreading excellence and widening participation”;
the Euratom Programme; and
the activities carried out by the European Joint Undertaking for ITER and the Development of Fusion for Energy for 2014-2020.
For more information, please consult: http://ec.europa.eu/research/participants/data/ref/h2020/other/hi/h2020-hi-swiss-part_en.pdf