As a rule of thumb I won't hire someone I wouldn't want to actually work with day to day.

Other than that, it depends on the balance, the person's awareness to his faults and his willingness to improve. Everything can be improved and it's often for the benefit of both the company and the person, so if he/she is willing to actively work on it (and of course if they are good enough in other areas so it's worth the investment) then it's enough to at least give it a try.

It depends of what kind of communication, for example for a developer it is really important to communicate any problems or issues at every stage of the project that is really important, also to express any problems that he might have at the start of a project or something like that but if your ex-boss were talking about talking and socializing with everyone everyday at every hour that would be just stupid, I've found that the people who does that a lot doesn't get the job done. It is ok to talk and joke with your co-workers but to speak all the time and doing just social stuff won't get you anywhere to complete any work at all.

Sometimes a lot of communication is not needed, let's say the developer can work without supervision, work remotely and a month later he delivers a product which is fully tested and works flawlessly - would it be a complete train-smash if that developer lacked proper communication skills?

If you adapt your processes to fit the developer's strengths, then you could make it work.

If his/her duties were to train other developers, give feedback to investors on a technical level, etc, he/she would be the wrong person for the job, if however the requirements were somebody to build special projects that takes months and doesn't require a lot of communication, that developer might be a great fit.