Be very careful though that you don't misinterpret what I said to mean that there is no value whatsoever in your English major. While over the course of a career you may draw on that experience - the same way, for example I draw on my military experience - more than anything else, what got you employed in this field was your CS minor, and what keeps you employed is your wealth of experience.
Being a good communicator is a bonus, but - sadly perhaps - I've never seen anyone get hired for their communications skills alone.
Not without any other relevant experience to speak of, no. I've seen good communicators beat out poor communicators, but there is almost always something else that makes them attractive to the employer as well.
There are many fields (for example media, PR, some civil service positions) where communication is the primary skill being assessed - written in the CV & spoken in the interview. If you have a non-maths written component to your interview, you're being judged on your communication skills/literacy.
I agree there is often something else required too - but not always in a 'first' or 'graduate' position.
To be honest, I thought it was rather obvious to those of us in this thread that if the primary technical skill for the job is communication, then having good communication skills is having good technical skills.
I believe the topic however centred around communications skills as ancillary to other technical skills that were part of job description.
Being a good communicator is a bonus, but - sadly perhaps - I've never seen anyone get hired for their communications skills alone.