I don't know if I'm aspie or NT for sure, but my take on it is that it is important to tell. You may not want to *right away*, but sooner is better than later. You would want to tell them before any kind of conflict comes up, for sure. To pull it out during a conflict sounds like a "get out of jail free" pass and an excuse for anything you might have done to contribute to the conflict. Better to say ahead of time that you're aspie and explain how you are different.
Someone who likes you is going to want to understand you better and do things that please you and avoid doing things that displease you, as much as possible. No one tries to go around purposefully offending people they like. So, the more you can explain yourself (preferences, patterns of behavior, quirks, etc.) the better. Though I wouldn't overload someone with a long list of things in one sitting.
I don't know what "knowing someone fairly well" means. By the time someone knows me fairly well, they will have already figured out I'm a bit off and decided whether or not they were going to put up with me.