UPDATE: Yes, recent model iPhones can absolutely use LTE data while on a voice call. The original answer below refers to the first generation iPhone, released in 2007:
Unfortunately, no. The iPhone uses the EDGE network for data communications. EDGE cannot be used at the same time as a voice call is active as these two types of communications utilize the same channel.
3G capable phones can transmit data and voice simultaneously without interfering with each other.