I can say from personal experience, I did my CS MSc (pretty much equivalent to MA in most places) without first completing a CS undergrad (BA equivalent). Therefore, @M.P.R is right about the fact that a CS grad course will more likely give you an MSc, not an MA.
Moreover, @JoeCorneli is also right that applying computing capabilities to real world problems is very different from becoming a programmer. Not all programmers are capable of plying things to the real world and not all computer scientists are actually very good programmers. Yet, I do not fully agree that a CS MSc will not teach you the application of programming to real world problems (in theory that should be the focus of a CS MSc).
That said, a CS MSc will not teach you how to program. You either need to be a decent programmer beforehand (my case, I had some 3-4 years of professional software house experience when attempting my MSc) or be very well self-educated in programming.
A good university will test you whether you are at an acceptable level of programming. They need to. During a CS MSc you will learn where computing meets the real world, and what are the fields where research is happening today. That will require you to be fluent in pretty much any programming language.
A hint of what (I believe) is a good measure of whether you are capable of attending a CS MSc without a formal education would be: (1) given a program in any programming language, that is not horribly obfuscated, you can tell more-or-less what it is doing; and (2) you can imagine how most applications are built on your desktop, or a server (you do not need to be capable of writing it yourself but you need to know, for example, why databases are built the way they are).