A month might make you able to write fairly complex stuff, but it won't give you time to learn the best ways to write efficient fast code and COBOL, despite its apparent simplicity, is remarkably easy to write nasty (self modifying if you wish) resource-hogging evilness. If you're on mainframes, it'll be longer than that before you've figured the full intrigues of things like Expediter, or, if you're really unlucky, core dumps, which can be your only way to debug.
I've worked with COBOL since the mid 90s, so I'm still considered a noob in the field, but I've seen some horrors written by people with twice the experience I have and I've rarely seen *good* code written by people with anything less than a year of it on their CV.
Bear in mind also that most COBOL is mainframe still, so chances are that as well as the language itself, you're going to have to learn DB2, JCL, CICS and suchlike. Mainframe assembly will also likely crop up in your radar and in certain financial institutions, PL/1 - all linked into one big horrible mess. You might think you'll learn COBOL in a week, but almost no company using it for mission-critical stuff will let you within a mile of their production systems until you've a couple of years under your belt.