From anecdotal evidence, it seems the teachers who are both subject smart and have personality are the ones who make a difference (and are fondly remembered). Conversely, those with bland-neutral personality or come off as negative never get a fair shake or remembrance from students.
Is teacher personality ever discussed?
I cannot speak for all education programs. ESL is a little marginal, and therefore wonderfully quirky.
We don't frame the discussion in terms of "personality," but rather in terms of "affective learning." Affective learning means making the classroom a low-stress, creative, humorous environment; bringing affect into instruction with teacher humor and creativity; and encouraging the students to be their own creative, individual selves. It means giving the students creative work in which they can construct their knowledge as individuals and as a group. It means giving the students some outlet for personal reflection, like journaling, and, if possible, connecting with students' families and communities.
Of course, all students would benefit if we gave affect some breathing room in the classroom. Affective learning is especially important for our English language learners, though, because they are making HUGE EMOTIONAL adjustments to their new identities and cultures. Have you ever studied a foreign language? Have you noticed, perhaps, that you sort of become someone else when speaking the new language? This person is still you, but this Spanish- or Portuguese- or Khmer- or Mandarin-speaking you might think about the world a little differently, and by definition expresses himself differently than the English-speaking you. Imagine that phenomenon times a hundred, plus pressure, perhaps, from a misunderstanding society to abandon your native language, plus pressure from your parents to maintain your native language, plus grappling with a new culture and how much of it to adopt. At certain times, you would be a bundle of emotions. The teacher needs to support you in this journey and to demonstrate the value of your culture and language.
On top of all that, Stephen Krashen tells us that anxiety is a barrier to language learning, and some theorists whose names evade me...Well, they say that imagination is the way to motivate a student to learn a new language. The native tongue already provides everything the student needs: security, communication, relationships, and so on. But the second tongue, oh, that can become a place of freedom and dreams, of whimsy and fun.
I think we frame this in terms of "affect" because affect can be changed or adjusted. Asking a teacher to alter her "personality" would be hurtful. But, we can ask teachers to change how they present their personalities, inviting them to share warmth and humor and imagination with students.