No, but you need to check where the provider's data centres are. A cloud service hosted in France or Scandinavia (with a decarbonised electricity mix) emits 5 to 10 times less than one hosted in the United States or Germany, and AWS, Azure and Google Cloud all publish emissions reports by region. The sound approach for an IT director is not to leave the cloud but to choose the hosting region deliberately for recurring workloads.
Read the source article: IT carbon footprint of a French company: where to act first