I will second what Dr. Fencer said! If you're looking solely to network, a great way to stand out is to go to a conference and introduce yourself to directors. Otherwise, like other posters stated, I would not advise contacting directors while applying just to get your name out there. I personally believe there is a lot more risk in that than reward, and your application will likely already speak for itself in ways that are more professional and captivating.
Another great conference that I'd add to Dr. Fencer's list is the
Southeastern Medical Scientist Symposium (SEMSS). It's a conference for those considering physician scientist careers, and it generally has separate events throughout the weekend (and then joint poster sessions) for both current MD or MD/PhD students and then undergraduate students who are thinking about MD/PhD programs. It is
run by the MSTPs at Emory, UAB, and Vanderbilt. I attended for the first time two years ago when I was applying to all three institutions, so it was a great way for me to meet current students, program directors/administrators, etc. I also had the chance to present my work to the director of one of the schools to which I applied, which was cool! It is at Emory this year in November:
Home (website).
Finally, I will also note that Dr. Fencer often posts on here when he will be attending a conference and is willing to meet up with SDN students over dinner, etc. If you are looking to meet a director, Dr. Fencer is very kind and gives wonderful advice, so I suggest taking him up on any offers!