I have heard of many folks who did the "Advanced Medicals". It has got both pros and cons. It is upto you to decide.
Adv : As you said , it will definitely chop off about a month's time in average, in your file processing; provided everything goes oout well and fast.
Disadv : You do your medicals now, and if by any chance, the processing of your file is delayed (There are 100 reasons you can find and so many examples from this site alone.); you might end up crossing the expiry date of your medicals (usually one year) and then have to re-do the medicals.