i don't think simply switching on automatic updates will affect battery. but what will affect it is how many apps actually update per day on average.
if you would have updated these manually during the day anyway, then there wouldn't be a difference. if you save updates till when you're charging, then of course, automatic ones may happen when you're not charging and use more battery.
if you are concerned, i would recommend enabling automatic updates but don't let it use mobile data. this will ensure updates happen when you are on wifi where a) downloading is less battery intensive and b) you are more likely to be charging your phone. best of both worlds imo. (and of course c, you will use less of your data plan, if you have a restrictive one)