No, it’s not necessary to fill in the form with the exact date of arrival. You only need to estimate the earliest time possible you plan to arrive but you completely can arrive after that date. The exit date is the last day you are allowed to stay in Vietnam unless you apply for Vietnam visa extension.
For instance: If you apply for 1 month single entry visa and submit your arrival date as 20th March, the visa letter will be valid from 20th March – 20th April. You can arrive anytime during this period of time but you must leave Vietnam by 20th April.