What happens if you send tether (USDT) to a bitcoin address?
USDT is part of the omni layer on top of Bitcoin.

While the transaction will go through (since any omni transaction is a valid Bitcoin transaction), you will not be credited for the USDT as GDAX is a USD exchange. They don't support USDT, and hence won't be trying to detect omni transactions for it.

You should contact GDAX support about how to recover your USDT.