Hmm..
In the case of our kit inside the barrel, the average density of the barrel has increased. The barrel will float a bit lower in the water (ie. it is now less buoyant)
In an extreme case – if I partly filled the barrel with lead, it would sink – i.e. negative buoyancy.
My guess is that this effect is not very significant if you are talking about a sleeping bag, but probably would be if you stuff the barrel with essentials like tins of beer and bottles of whisky.