Well.... I'd imagine that if you have a lot of weight in the handlebar bag, and no other bags at all, and the bars are set very high, it might get a little wonky.
Overall though the long wheelbase (and iirc fork geometry) are designed for stability. So I can't think of a reason why the LHT would be any different from other touring bikes in this respect, unless the bars are very high.
By the way, if you want squirrely, try descending at 30mph on a 20"-wheeled folding bike with a handlebar bag.
