Can I run traces through "No Connection" pins?
It's a grey area. Some manufacturers tell you that's used for calibrating. Some manufacturers even will tell that you that certain pin has a function, only used by them for calibrating. Some tell you only not to connect it, or just say it's an unconnected pin.. You can't know for sure. The datasheet is information the manufacturer want to tell to you about using the device, but it might not be everything.

I recommended you do not connect them. If you get some generic IC from a different manufacturer or even batch the behaviour might be different. If you're engineering a project, you don't want to throw in unpredictability. You would have to test every single batch before you're going to use that particular batch. It depends on whatever you want to do that.