The simple answer is yes. If you plead or are found guilty of DWI, you can never completely wipe it from your record.
However, depending on the facts of your case and the time surpassed, you MIGHT be eligible for a non-disclosure. If you are eligible, this will not completely erase the arrest or conviction. Government agencies and law enforcement are still able to access these records. This might potentially allow you to seal/ hide a past conviction from future employers and from public record.