The difference depends on whether the character of this person has been defined.
You may have already said that you, or the person concerned, is a 'high-achiever', with ambition and drive. This would suggest that 'such a person' would not be willing to work in a job which offered little prospect of advancement. The use of the word 'such' in the phrase 'such a person' emphasises that (s)he is not the type of person we might expect to stay in this job.
if you omit [leave out] the word 'such', then the question could apply to anyone, not just the person concerned. You would be saying that the job is so demeaning that anyone, whether ambitious and high-achieving or not, would be frustrated and want to quit.