Here's the official Verizon policy on obtaining the SIM unlock code (as of March 2011):
So as long as you've been a VZW customer for 2 months, you theoretically should be able to call VZW Global Support (908-559-4899 or 1-800-922-0204) on day 1 and get the unlock code. In all likelihood if you're nice they might even give it to new customers.
Not being a Verizon customer (yet) I called the Global Suport number but since I wasn't a Verizon customer I got regular support. I asked them if the unlock was permanent & they said it would be locked again when you put your Verizon SIM back in after returning from your trip. I would like a VERIZON customer to call the Global Support number & ask them exactly what does this mean;
"Only one SIM Unlock per line every 10 months"