Yes, Poeltl would have to be part of any package for KAT. It's hard to get an All-NBA level talent without sending back a replacement starter, and KAT would eat most of the minutes at C anyway.
I don't buy the whole "loser mentality" or "soft" stuff with KAT either. AD had very little playoff success in New Orleans but is a legit superstar. Pau Gasol didn't win a single playoff game with Memphis and was Finals MVP level with the Lakers. If it takes Poeltl + White + two 1sts to land KAT I'm all for it.
Minnesota can doubtless get a better deal, though. I'd be willing to give up more, but I'm not sure how much more.