Possibly.

On March 22, 2020 ENTUK, the professional association for Ear Nose and Throat surgeons in the United Kingdom, published a letter to Public Health England (the agency mandated with protecting the health of people in the United Kingdom) citing loss of smell as a noted symptom of mild SARS-CoV-2 infection. The purpose of the letter was to encourage doctors to wear full personal protective equipment when attending to patients, and to recommend that patients with a loss of smell quarantine for 7 days.

The SARS-CoV-2 evidence in the letter includes several statements about the high incidence of loss of smell in patients, though the data itself is not specifically cited. However, loss of smell and taste despite not having a stuffed up nose is a common symptom after upper respiratory infection. Over 40% of all cases of loss of smell are thought to be due to such postviral olfactory dysfunction. A number of viruses are implicated in causing neurosensory damage that can leave these senses diminished for months, including coronaviruses. Coronaviruses are known to infect the central nervous system and cause neuronal death. Moreover, the olfactory bulb (the brain structure inside the roof of the nose that receives odour information) has been shown to be a coronavirus route to the brain. Combined, this information suggests loss of smell may be a symptom of COVID19 and a very broad mechanism by which it might occur.

HH and JFB March 24, 2020