Most people I know recognize that it is pronounced like "ah-nee-may" as opposed to "ah-naim". There might be some who would mispronounce it like that, but I doubt most.
In any event, why would anime, a Japanese term, have an accent in it? Sure, it's a reduction of animation, but that word has no accent as well, plus the fact that it started in Japan. So, there wouldn't be an accent anywhere.