Can I answer no to the question in the application if I successfully completed the diversion program last week?

You say, "This was my first DUI." like its no big deal - it really kinda is and will very likely have a big impact on your ability to get a job. That said, in North Carolina a first offense DWI is not a felony so if the question on your application only inquired about felonies, then you would be able to honestly answer no. However, a conviction of DWI will likely always pop up at some point so it will generally be the best policy to be upfront about it with any potential employer. And upfront in a way that lets them know you understand the severity of a DWI and will not let that happen again. The logic behind taking this approach is this - any potential employer who even half way checks into your background is going to find out about the DWI whether you disclose it or not so if you are to have any hope of the DWI not keeping you from getting the job it will be because the employer was impressed with your honesty and candor.