가입 후 이메일 주소를 변경할 수 있도록 허용 - 새 인증 이메일이 발송될까요?

I noticed this setting “Allow users to change their e-mail address after registration” in “Admin → Users”.

If we tick/check this, the user will be able to change email. My question is, will the new email address receive a new verification email so the site can verify this new email address belongs to the user?

Yes. You can try here by changing it in your profile. Staff users have to verify having access to both emails the old and the new one.