I can tell you from a personal experience: absolutely not!
I attended Computer Science (Bachelor + Master) and I am currently working in a good Software House. To find a job was not so hard and I did not have to wait long before finding a good place.
A friend of mine shared with me the same flat at the university and he was studying philosopy. He got his Master Degree in Philosophy with a reasearch on Artificial Intellingence.
Now he is actually working at MIT in Boston! Therefore it does not matter your background, if you are skilled and good in software area it will not be a problem.
Unfortunately many HR people, receiving daily hundreds of CVs for a single job, tend to adopt strict criteria for selection, since they do not have time to scrutine all the dossiers.
But this is not always the case, if you have a chance to get an interview, then you can good present your motivation and knowledge (that is what companies search at most).