*Going to necro this a bit, since deadlines are upcoming.
There is a definite caveat here. While contacting potential advisors might not give you an advantage, in the sense that it strengthens your application, applying out of the blue is not something I would recommend either. The departments I am familiar with absolutely recommend reaching out to the faculty, at the vary least the DGS. Sure, some "old school" professors might act like they are too busy for your inquiry, but in my opinion this is the exception to the rule. If anything, it helps you get the lay of the land. Will your potential advisor actually mentor the research you are proposing (their bio really means nothing to this effect - research interests change faster than university websites in some cases)? Do they have a sabbatical or fellowship year upcoming? Or, is there merely an internal hierarchy where junior faculty admit students less often, thereby making it more difficult to admit you - in my experience faculty are quite honest about this. However, in most cases, you will usually receive a polite response suggesting you look elsewhere with tips on the search, a positive reply with an invite to chat over Zoom/Skype, some other helpful piece of advice, and most of all, s/he now has an awareness of your application as it comes through the system. This, if anything, is worth the short time investment to send an email.
NB: written from the perspective of an archaeologist.
