Fireblocking a balloon framed house lead to rot in the walls?
If you close off the bottom of balloon framed stud bays, yes you will impede the flow of air from basement to attic.  However, water vapor may still be able to escape through the sheathing, tar paper, siding, and paint.  Old houses tend to breathe quite a bit and take a lot of work to really seal up.  It would be hard to say how well sealed up your house is, who knows how it was built and what's been done since 1930.  

I might be concerned that there may have been some minor leaks or seepage that were draining down the wall cavity to the sill.  With the bays open, these might have dried without causing any trouble but with less air flow, might soak the insulation and rot the sill or bottoms of the studs.  If there's any seepage like that you can probably spot some dampness after rain or some darkening of the wood.  

You could pull some of the bats in the basement occasionally, especially after storms, and see if it looks like there's any trouble - dampness in the bats or the framing.