Based on talking to a couple of admission directors, most programs do not reject or negatively mark applications on grounds that there was a delay in receiving transcript, GRE score or recommendation letters. So, no, it is not wishful thinking on your part. However, if your application is completed so late that the committee members do not get the time to read it before their first meeting, your chances will obviously suffer. How late is that is something that I dont know, and may vary from program to program.
At this stage, I dont think you have the option of submitting any application way before its deadline, so maybe you better not worry about that.