It looks like Coinbase and Gdax is owned by the same company. Even log in and pswd is the same for both. So, yes you deposit USD not USDT(because Coinbase doesn't support it) into your UDS wallet and can instantly transfer it to Gdax for free with no limits. And go from there. It is a lot cheaper.

What i find out you can transfer crypto between Coinbase wallets for free and it is fast and user friendly because you can use just e-mail address for a recipient or BTC address.

Gdax doesn't charge me to withdraw to my Coinbase wallet, here you can find what are the fees on GDAX.