There are two sides to this question and therefore two answers.
First, in terms of whether you should apply before completing your MBA or wait until you have graduated, it depends on what your present academic standing is like and what your schedule is like. It is generally accepted that you can apply for jobs before you complete the course. If you already have a good academic record and/or have some good results from your first year/term of the MBA, then you can use these in your application. If you need a good result from the MBA to strengthen your academic rating then you might be best to wait until you can put the full qualification on your CV to avoid all doubt in recruiters' minds about your ability to finish the course with a high score. If you complete your exams in May and have a relatively open summer (e.g. for coursework or a project) then you will have more opportunity to schedule interviews. If you will have to work hard and have a busy academic schedule then the stress of trying to schedule and attend interviews may not be worthwhile and you should wait until you can give your job applications your undivided attention.
Second, in terms of when the Big 4 will accept your application, you can apply whenever you see a job posted on the website. When you go through the online application process it actually says whether the job is still available. The Big 4 are usually quite good about taking jobs down when they are filled. Should you apply just as the post is filled, it won't count against you as a "rejection".