More than likely, you will be ok with down, though you will need to be prudent. The southern AT in late winter/early spring offers a damp cold which over the course of several days can basically seep into your bag and cause a minor loss of loft. This is not the catastrophic loss caused by immersion, but it IS a factor.
However, since most thru-hikers normally hit an outpost of civilization once a week or so, airing the bag out in a warm dry place overnight generally solves this problem. To avoid the danger of full immersion, I use a trash compactor bag on the inside of my pack ALWAYS. For the AT in Spring, I would also recommend either a poncho or pack cover.
Rain can be continuously drizzly for days. Use of shelters generally means a dry place to sleep BUT I only got space in a shelter maybe half the time my first few weeks out due to heavy hiker traffic. I used synthetic on my thru-hike eight years ago, but I would use down now, and simply be careful with it.