No. People with COVID-19 who have symptoms should wait to be vaccinated until they have recovered from their illness and have met the criteria for discontinuing isolation; those without symptoms should also wait until they meet the criteria before getting vaccinated. This guidance also applies to people who get COVID-19 before getting their second dose of vaccine.
People who have had a known COVID-19 exposure should not seek vaccination until their quarantine period has ended to avoid potentially exposing healthcare personnel and others during the vaccination visit. This recommendation also applies to people with a known COVID-19 exposure who have received their first dose of an mRNA vaccine but not their second.