You know, thats a very good question. And I've never asked, nor seen it asked that way.
The answer I would have to say is still yes however, because there will always be, even if its brand new, some Fe oxide on the brush, the rust would be greatly minimized as opposed to a brush that has been contiminated with Fe oxide from CS base metal.
Its the oxide and not the Fe. SS has lots of Fe in it-it is a ferrous material. ~70% to 75%.
No ! The HAZ will rust before the weld will.Just use the same brush you started with to brush the 309 weld and don't use it on stainless material after you have used it on the stainless to carbon.Have one carbon brush,one stainless brush,if you are welding other stainless material like 316,308,etc.dont use it on the 309 material.You use the same brush on carbon material and on the Bi-metal weld.I Would use a brush that has stainless wire on the brush.I have welded hundreds of these type welds in power house plant's.I would use a stainless wire brush,but I also had another stainless brush for stainless material only.Just mark them up.I hope I have not confussed you.