Yes, it is possible. It's not easy to block, either, since an attacker can forge the source IP to be one of almost four billion IPs. However, a lot of attacks such as this can be filtered by examining the DNS data inside the datagram. A lot of flood attacks either use invalid data or use the same data over and over again. This can be used to differentiate the valid traffic from invalid traffic if you have network equipment capable of deep packet inspection. The attack will still use quite a bit of your bandwidth, but you can at least keep it from overloading your nameserver.
Normally, though, the nameserver itself is not the target for these sorts of attacks. Instead of using a random source IP, the source IP is set to that of the real target: a DNS reflection attack. Very short questions resulting in long answers are sent to the nameserver, and the nameserver sends the answer to the target IP address, flooding it with traffic. This is easier to filter on the nameserver side since it appears as a single source since it is so targeted.