Great question?and the answer is ....generally no but it depends on who you are and how well you got on with people when you worked,I know of two tl who were rehired months after walking out and being put on the no rehire status,but in both of those cases after being refused at the store they appealed to the dtl and were rehired,I know of one team member who refused to take a drug test after having and accident and quit,a few months later i saw him working at another Target.In those three cases all were excellent workers and there were no ongoing issues with them.
So where do you stand? you should know yourself,if you got peoples back up your chances are very slim,good luck either way.
At least at the store I worked at it depends on how desperate they are to get bodies in the door... Didn't work so well last year when HR decided to hire on 2 that were on the no-hire list from a couple years back. One of them NCNS for orientation and the other called in like 4 times in the first 2 weeks and was termed (mysteriously similar to the reasons that they were on the no-hire list!)
As far as I know my store is not going to hire anyone that is on the list anymore. But if it has been a few years, you have a stable work history, and what you were termed for I don't see why you wouldn't be able to talk your way into a job with spot. But then again I am not psychoanalytic expert on the ways that Target thinks