I'm not sure what exactly an NACLC check looks into, but you will be denied a CCW if you've been convicted of a felony, domestic violence charge (the DV arrest may be enough, even if the case was dismissed as one of the members here is having an issue with currently), two alcohol related convictions in the last year (maybe two), if you're currently under investigation for a crime, or if you have a protection order taken out against you. Depending on which county you live in, there may be some discretion to deny a permit as some sheriffs are more anti-gun than others.
In general, I would think that if you can pass a federal and local check to get a security clearance (the extent of my knowledge on NACLC checks) you should be able to pass a CCW check. You may even have a quicker turn around as your prints are likely on file at least once and will be easier to match.*
* - Last two sentences are just my impressions and I am not an expert nor a lawyer, I just try to be informed. If anything I have said is incorrect, anyone with more knowledge please correct me and I will adjust or delete erroneous information.