What if I were to rack wort over beer that had basically finished fermenting? Or would the yeast not be interested?
I'd make all wort additions before or at peak krausen. Adding new sugars to yeast that are going dormant is just asking for off flavors.
What specific off flavors would be involved?
Adding new sugar over a period of a week or so is common in raising the alcohol content of wine without any effect.
I would recommend adding any sugars to the wort either before or after fermentation, but not during. The main reason is that the first thing the yeast will ferment is the simple sugars (glucose and fructose), then it will switch to more complex sugars (maltose, maltotriose, etc). The presence of glucose inhibits the fermentation of the more complex sugars. If you add additional glucose while it is fermenting maltose, the cells will stop fermenting maltose and switch to glucose. Wen the glucose level drops again, they will switch back to fermenting maltose. This may
have an affect on the overall fermentation performance, and might not give repeatable results.
Adding sugar at the end though, seems fine to me. I do it when I (rarely) add fruit to beers, the yeast don't seem to mind. I don't have a lot of experience with it though.