As Mr. Pate alluded to, make sure you carefully read what the question is asking you and answer truthfully. If it asks about convictions and you have successfully completed your DA and received a dismissal, then you are not required to disclose. On the other hand, it if asked whether you have ever been arrested or charged, then you must disclose that fact. It will remain on your records unless you are eligible for and receive a full expungement of the record. You must be truthful because, as Mr. Pate also stated, lying on the application in and of itself could result in exclusion and/or sanctions.
As the other answers have stated, read the questions on the application carefully, and answer truthfully.
In Oklahoma, there are really three stages of your deferred sentence you need to be aware of ...
First, once you have pled onto the deferred sentence, the case will show as an open and pending case with a guilty or no contest plea during the deferred term. During this time, the court record is open, and anyone who looks for it will see that you have pled guilty/no contest and started your probation.
Second, once you have successfully completed the deferred period, your plea in the case will be changed to a not guilty plea, and the charges dismissed. At that time, your court file is sealed/expunged, so it would not be available for the public to see. A check at that time will show no record with the court of your prosecution at all, and your OSBI arrest record should be changed to indicate you were arrested for the charge and pled not guilty, with all charges dismissed.
Third, in Oklahoma, two years after the successful completion of your deferred, if you have no other arrests/convictions to disqualify you, you may petition for the expungment of the arrest record itself. This will erase the OSBI arrest record, the law enforcement reports, and other public records of the case. This expungment statute states that the offense shall be treated as though it never occurred, and prohibits use of the records if anyone does know of them.
Which stage you are at in the case determines how you should answer the questions, so read them carefully.