The copper vs steel subject rears it's head far too frequently, here is the real story.
It can be said with great certainty there is virtually no difference in heat transfer if Copper vs. Steel tubes are used in a small steam boiler. Having worked as a professional engineer in the heat transfer, fluid mechanics, and thermodynamics arena for nearly 35 years, and, at least in these realms, this is the real technology.
A very reasonable analogy can often make this more clear. Let us say we are having a traveling race, having three separate segments, for 9 miles total distance.
The first 3 miles of the race is done with brisk walking, on foot only,
The second segment is using any motor vehicle you like, and is also 3 miles distant.
The third segment for the remainder of the race, again three miles, and you use a good horse.
In this analogy, the first segment of the race, on foot, represents the travel of heat from the flue gas to the surface of the tubes, and this process is by far the greatest resistance to travel, at 3 MPH, taking about 60 minutes time.
The second segment of the race, with any motor vehicle, say a Ford Pinto, or a new Corvette. This represents the travel of heat through the tube metal, Steel tubes (Ford Pinto) or Copper Tubes (Corvette). This process, takes 3 minutes for the Ford, at 60 MPH, and only 1 minute with the Corvette at 180 MPH.
The third segment of the race, with a thoroughbred horse, represents the travel of heat from the tube surface into the boiling water, a traveling method far faster than walking, but much slower than the automobile, say 30 MPH taking 6 minutes to complete.
So in this travel race, the entire three segment trip with the Ford Pinto takes 69 minutes, and with the Corvette 67 minutes. While the Corvette is wildly faster than the Ford Pinto, the overall trip time is virtually no different. Yes, the Copper tubes do make better heat transfer, but not in any way significantly.
As to the question of using a tube material with even lower thermal conductivity than ordinary steel, for example, stainless steel, which has a thermal conductivity about 40% of ordinary low carbon steel, the answer remains the same: The tube material has virtually no significant impact on boiler steaming capacity, be it copper, or carbon steel, or stainless steel. The conductivity of tube material is not the relevant resistance to heat flow from the fire to the boiling water. The heat transfer coefficient getting fire heat to the surface of the tube is the real "bottleneck" of the process, while the metal tube conductivity issue is one or two orders of magnitude less important here.