A Class C is the only type of deferred adjudication that can be expunged if successfully completed. A Court order granting an expunction specifically allows you to deny the occurance of the arrest, etc except when you're asked in Court under oath.... at which point you have to acknowledge that the matters inquired about were expunged. Consult with the attorney that obtains your expunction specifically about your licensing application.
If your plea was for a class C misdemeanor and if the case was dismissed after successfully completing deferred adjudication you may have the charge expunged. This would erase the record of your arrest and you would be able to legally deny the event ever occurred. Call me if you need any assistance in this matter.