Only marginally. Deleting 1,000 emails saves about 5 g of CO2e (server storage), whereas the time spent sorting them (30 minutes of a PC switched on) uses 28 g of CO2e in device energy. A more effective lever for email is to cut heavy attachments (a download link rather than a 10 MB PDF) and to unsubscribe from newsletters you do not read, which reduces the incoming volume.
Read the source article: Website carbon footprint: how to calculate and reduce it