Even if you could, the problem would come when you wanted to establish a data connection with the remote end. Assuming "except for DNS traffic" actually means "

Even if you could, the problem would come when you wanted to establish a data connection with the remote end. Assuming "except for DNS traffic" actually means "except for packets on the well-known port for DNS" then you are going to be restricted to sending packets with destination port 53. This means that for comms to work, the remote end is going to have to be able to receive packets on port 53. Some kinds of network setups may allow this -- all of this stuff ends up being hideously dependent on the detail -- but many won't.