Yes, the 3G use is free. If your Nook cannot connect to a known wi-fi, it connects via 3G without requiring user intervention. Below is copied from the B&N Tech Specs of the wi-fi/3G Nook:
NOOK 3G+Wi-Fi includes FREE wireless connectivity via AT&T, the nation's fastest 3G network - with no fees or contracts. *
*Available now in over 190 U.S. cities, AT&T 3G Wireless service provides accelerated data speeds and data capabilities for an amazing wireless data experience.
Disclaimer: 3G network not available in all areas