The answer as proven by multiple members on here is yes. Actually that's not quite true, the real answer ultimately depends on the dealership and the area you live. A trade in where you live may go for 15k, but where I live would go for 20k or the other way around for example. I answered your question in the post you quoted by the way, "I guess it really depends who you sell to".
I was more posing a hypothetical question, assuming everything else is equal. I've seen some dealers run carfax and pickup an accident report, and others, take the same vehicle on trade without running a carfax and noting a accident, so, to your point, it depends. But, there is definitely the potential, that down the road, this could impact resale value.
You are however, confusing VW and a dealership. The two really have nothing to do with each other in the way most people think. When you trade a car in, you are dealing with the dealership and not VW. Not sure why that is so confusing for people.
Also not sure why people are confusing "rebuilt" and re-manufactured.
I'm not confusing the two. I understand the warranty is through VW and not the dealership, as well as the difference between used, remanufactured, and new. That's why i posed a hypothetical question, same exact car, sale dealership, one with a service record of a replaced engine (regardless of replacement type), the other, without. I'd think, if said hypothetical dealership pulled the maintenance records, the car with the engine replaced would take a hit. Maybe I'm wrong, IDK. But I think that potential is there regardless of the replacement type.
OP isn't getting a new car out of this. He might be able to get a new engine, although that's doubtful based on what VW is telling him. He probably has a better chance of getting an extended warranty or some other compensation. That's the approach I'd take at least.