For the candidates who compete for the same position, assuming their English is good enough to express the points, the opinions, and the thoughts clearly enough for others to understand, and to get others’ points without misunderstanding, the solid working experiences are more critical. You do not need to be a talker. The one who has the most related working experience would have more opportunities to stand out.
If I had a master degree, or even a bachelor degree, in accounting, and more working experience in the related field, the situation would be totally different.
I am not saying that my English is perfect. I agree that we can never compete with the native speakers. But the biggest barrier for landing a more decent and high pay job is being lack of the related working experience, but not the language limit.