I just visited the store in Manhasset, NY store with my brother. I will be out of the country on March 31, and further more, I'll be in China in a second tier city with terrible internet. The saleswoman at the store made it sounds like it would not be a problem at all to have someone make the reservation on my behalf, as long as I gave him my cc details. I am a bit skeptical (but encouraged). If anyone gets a definaitive answer from Tesla HQ, I'd love to hear it. I'd suspect this issue won't be cleared up until a few days before March 31.
Another issue, how is gonna work for anyone (in person or proxy) to make a deposit on March 31, esp. in the Eastern Daylight Savings time zone if the unveil is after the time most East Coast stores are closed.