juniorj, I don't think it matters too much. My DS mailed in the ones that where too far to drop off by hand. One MOC's local office was around the corner so we dropped it off in person. Didn't much matter, didn't meet anyone besides the receptionist. Nice enough person, but not influential.
I say it may be more important to follow up with phone calls. You may be more likely to speak with someone that is closer to the process. You can also begin to establish some contact with the office to make sure things are getting received, anything else that's needed, etc.
What's interesting is that our MOC representative told us a few things about the process that you may not find out otherwise, nothing critical, but things like "don't pay money for the SAT test score, just send in a print out from your computer". Call and let them know you are interested in making sure the process goes smoothly for everyone.
I'd say what's important is to send things USPS Return Receipt so that you get a return card to assure the package got to it's intended recipient. Keep copies and records, of EVERYTHING, no matter how unimportant you may think it is. Everything you send will be important.
Good luck and don't forget to breath on occasion through this process, it can feel like a long haul.