I have never seen or seen data that tells me that carbon in the lower ranges has an effect on corrosion rate.  At one time all C/S corrosion test coupons were made from 1018-1022 C/S. As the availability of commercial coupons of specific materials became available the trend is to use the actual metals. The 1018 C/S coupons are still used.  As your approach pure iron there is some change in the corrosion characteristics of the metal.  As you go higher you can measure different corrosion rates between say a 1020 versus a 1095.  It not usually significant.  And these are specific cases.  The environment determines whether there is a difference and how much.  
This is not a good statement to make but it’s is true in a practical sense, “carbon and low alloy steel will corrode practically  the same under most conditions until the Chromium content gets to 10%-12%”. This is limited essentially to ambient temperature and pressure. There are exceptions to this statement that have to be dealt with on an individual basis.
A common example is a knife blade will rust if its 1075(cheap) or (1095)costlier and this is true even with S/S steel knives the cheaper ones will rust(10% Cr) the more expensive 15%-20% Cr take longer to rust.

Corrosion can and does get very complex quickly.  I would try and get a book on corrosion fundamentals if you want to learn more about corrosion.  I one is not in materials or is a corrosion engineer the biggest lesson to learn is “When to ask for assistance”.   

Look at:

www.nace.org

www.asminternational.org

Look at their book stores.