No.
The tornado brush is stainless steel and is much harder than the wrought iron - very low carbon laminate. In the unlikely event that the brush would fracture, you will get a long gouge in the bore.
I communicated with Breck Gorman about this issue 1 month ago, and at that time Amazon listed a Pro Shot
brass tornado brush, which is what I have been using.
It is no longer listed 
I would stick to a phosphor bronze brush.
One of my damascus barrels is pitted and a real pain to get clean. Hoppe's Elite Bore Gel helps alot.
Frontier Big 45 pads are an alloy of stainless steel, nickel silver, monel (a corrosion resistant nickel based alloy), and zinc, and are softer than stainless steel wool - if it won't remove blueing, it won't remove bore metal.
When wrapped around a jag on a rod chucked in a drill it works very well with the Bore Gel
https://www.big45metalcleaner.com/