If you are accepted, then you do not have to worry about applying to other medical schools. You will be stress free because you would know what medical school you will attend next year. If you do not get accepted, you will apply normally like everyone else. Applying early can never hurt you, it can only help you.
The only word of caution is that you must make sure that the school that you apply through early decision is a school that you want to attend. Remember, if you get accepted, you must attend that school.