hm, In another re-invention, I was a recruiter for five years. My advice: great start, but push a little. Don't wait. Call your contact and find out the name of the person who "app is in" with. See if your contact has enough influence to get that person to set up a meeting with you on their recommendation alone. If not, ask your contact if he or she would mind (or if he/she thinks it wise) if you call the decision maker yourself. Introduce yourself, acknowledge that he/she must have many resumes (and other things to do, besides) but you wanted to just introduce yourself and let them know how very interested you are in taking on this position and was wondering if you could schedule a short introductory meeting (not "interview").
Even if they say, "no," or "I haven't even looked at these resumes, yet," "we'll be in touch, etc.," say "I understand completely. Would you mind if I check in with you next week (day, date and time)?" If they say yes, call back exactly on that day, date, and time. If they say no, say, "I understand, thanks for your time, I look forward to meeting you." Follow up with the same thing in a snail mail thank-you for their time and a "in addition to my resume, I'd like to call your attention to the following significant accomplishments (or qualifications) that I will bring to this position." Then stay on top of your contact.
But you probably know all this: This just re-fired all my dormant recruiter synapses!