It is perfectly possible to stammer while at the same time having good or excellent communication skills. Fluency should not be seen as a precondition to excellent communication skills.
‘When, during an interview for a sales assistant role I mentioned the fact that I had a stammer, my potential employer replied “The fact that you stammer makes no difference to me, my first impression of you was very positive. You have the right skills and experience for the role, are assertive, and an excellent communicator.” She offered me the job, and whilst working for her, she also once told me I was the best sales assistant she’d ever met!’
Job talk (stamma.org), 2010.
A lecturer with a stutter (sometimes very severe) was voted by students top lecturer at his University and 14th in Australia, out of more than 6000 nominated.
The case of the stuttering lecturer (stamma.org) by Grant Meredith, 2009.
“Christine manages more than 20 staff in Brent Library Service and she is an excellent communicator! This may seem an unusual statement about an employee who stammers, but good communication is about what you are communicating and not just how it is delivered. Her approachable and interested style also helps communication.”
Head of Library Service, quoted in Recruiting and developing employees who stammer (archive of stammering.org), 2001.
In the Ohio firefighter case (a US case), the claimant could communicate at a blazing fire and was rated ‘excellent’ by colleagues, but was turned down because he stammered in the interview. The US court held this was discrimination.
The BSA website encourages candidates who stammer not to be put off by employers listing good communication skills in a person specification (Job hunting & interviews (stamma.org), scroll down to Communication Skills).
However employers should consider whether communications skills they specify are really required for the job (Examples of reasonable adjustments: Recruitment>Excellent communication skills), and consider how to assess communication skills of someone who stammers.