To answer this question you have to look at the laws of the state that you reside. Whether or not you can get your license depends on a couple of factors. Regardless of whether it is un-disposed, it will show up on your record. When you have met all the requirements to get your CNAS license usually a background check will be required. Most states have specific requirements for CNAS.
For example, some states will require additional paper work to show the circumstances of the DUI and the progress made since receiving it. In the event that you lied on your application about said DUI that can be grounds for denying you the ability for getting you license. In California, the Nurse Practice act considers an unprofessional action, like a DUI reasons for discipline. This could mean a delay in getting your license with a chance to appeal. If your DUI is in the past, meaning a few years back, they will consider those facts. The process of obtaining a CNA license is quite difficult and is important you disclose this information from the very beginning.
Everyone makes mistakes, but it is big ones like this that can keep hurting you after the fact. Usually a DUI in the past will not affect your ability to get you license if the proper steps are taken to show improvement. In the event you get a DUI after receiving you license the process will be very different. A DUI will remain on your record for seven years as long as you are truthful on your application there should not be a problem.
Remember to check you state requirements to make sure there are not any additional steps needed for your particular program. In the event that your state does decide on a case-by-case basses you will need to have more details to provide and the reasons the case is un-disposed. With most states, it will be a simple yes or no. Making sure you do your due-diligence will make sure you do not run into an issue with it later on and that you will not get them taken away after you worked so hard to get them. It will also do you some good to speak to a lawyer about your options, and maybe they can work out a game plan for acquiring your license despite the DUI.