Not necessarily. Most hosts buy guarantees of origin (GOs), financial certificates that do not guarantee that the electricity physically consumed is renewable. A host in Germany that buys Danish wind-power GOs still consumes electricity from German coal-fired plants. The criteria that matter are a published PUE (below 1.3 is good), a location in a country with a low-carbon electricity mix (France, Sweden, Norway) and transparency on water consumption and waste heat.
Read the source article: Website carbon footprint: how to calculate and reduce it