I think so. If you transfer from your wallet to Bittrex, the transfer goes into the Bittrex wallet. The memo code allows them to credit you the right amount on the Bittrex site, but the funds should still be in the Bittrex wallet. When you withdraw it comes out of the Bittrex wallet and back to your own wallet.
Similar with Binance, except I think the Binance wallet name had been taken, so it's deepcrypto8 (with the name cpzhao, which I believe is the CEO).
Interestingly, if you had been watching the deepcrypto8 account on Steemit, you could have seen them testing Binance transfers a couple of days before the official listing. Always pays to keep your eyes open!