I think there are rods specifically for this- either 308 or 309, I forget which- one is used for stainless to stainless, other for stainless to carbon.
One issue is that you can have dissimilar metal corrosion, which would tend to corrode the carbon steel. While I know this CAN happen, I've never heard or seen anything that predicts how fast this happens, or if it's a problem in a specific application. And of course, you're contaminating your stainless steel, which reduces corrosion resistance of it.