I don't own a syn bag. All mine are the highest end down. My thinking is..ones bag, is ones very last and THE most important resource, luxury, and sanctum, thats protected and kept dry no matter what and under ALL circumstances. That is first and foremost priority.
Hiking in the rain, snow, etc? I place the then stuffed sack bag into a trashbag(or 2) before placing into the very bottom of my pack. Then if it rains enough even to saturate the pack, its still good to go. Even setting the pack on the wet ground can and will soak the bottom of it and potentially get to the bag, so this protects its then also. Camping in the wet and humidity? I don't take the bag out of the stuff sack until shortly before actually getting into it. Just enough time to let it get to full loft.
Make sure no part of the bag is ever touching the tent walls.
NEVER place a trash bag or similar none breathable something over it. It WILL get crazy wet by morning. The most I've done is lay my breathable shell jacket over the foot box, and even then I was careful to not do it for very long.
I've been backpacking in the wet(we'd hear from the weather man of a front coming thru, and rush up to the mtns, specifically to get in the way of it. to be under siege, so to speak. just fun to do sometimes) for a life time really, and more then most will ever go. Some trips where it rained for days, and days, and days:thumbdn:. And I've
never ever had a wet soaked down bag, or even been cold in one for that matter. Never. The worst was killer storm at 6100' up on an exposed bald in NC..while in a Marmot Asylum singlewall(that was recalled because the waterproof breathable membrane..wasn't waterproof) that was leaking thru the tents walls, and shaking off (the tent was being pounded by 50-70mph winds) all over the bag, gear, everything. I waited until late to pull the bag out. The bag got pretty wet on the outside(which WILL give "some" defense) and did get to a good bit of the down but not soaking it yet. But even then, it still maintained a lot of it loft, I was still warm all night. Luckily that was my last night on a 5 day solo trip.
Remember, even IF you get the bag truly wet..the worst you'd have to do its get out of it..put your layers back on..make some hot coffee, food, etc, and wait till morning

. won't be fun, but you'll be ok. Hopefully the weather will be clear enough to try and dry it out somewhat..or just hike out..etc. Regardless you'll be good until its time to sleep again lol.