I agree with Chuck, if after repair you find the area around the weld to be hard to strike off, anneal it properly. Yes barrel steel is relatively soft if it were to hard, it would be very brittle. Just remember when undertaking a project such as this to use someone qualified. The brass internal chill bar will help with hardening as brass will soak up some of the heat and keep it from spreading outside of the weld zone. Filling the void between the bbls is not going to help that much unless you use something tougher that the barrel steel itself. I wouldn't recommend this as it will likely cause a violent rupture somewhere else. Ever seen a barrel fired on an ultra slow motion camera? Suprisingly enough the barrels actually expand ever so slightly and then return to original shape after pressure has tapered off. The elasticity of the steel allows this. I certainly would not want to compromise this with some kind of hard backing material. Just watch your hardness and test with a file, anneal if necessary.
