NTP uses UDP, and it will accept a domain name as the server parameter (not documented in the reference pages). Insure you evaluate the return value from beginPacket as 1 for success, and anything else (0 or negative number) as a fail.
This is from EthernetUdp.h.
// Start building up a packet to send to the remote host specific in host and port
// Returns 1 if successful, 0 if there was a problem resolving the hostname or port
virtual int beginPacket(const char *host, uint16_t port);