Yes. However, the chances are slim. Your Vietnam visa application will be denied only if your name appears on the Immigration Department's blacklist. If you have a good immigration history in Vietnam, you are not at risk. The Immigration Department has no reason to reject your visa application.
On the other hand, even if you have a valid Vietnam visa, the airline staff will not allow you to enter if you do not have a national passport valid for at least six months and a Vietnam e-Visa. It is recommended that you print your Vietnam e-Visa before traveling to the international airport. Please make sure your passport is valid for at least 6 months after your arrival in Vietnam.