Only if you send it to a wallet that you don't control directly.  In this case, he sent it to an exchange, which means only the exchange knows the private key of the BitCoin Cash Wallet.  If you had accidentally sent Bitcoin to a Bitcoin Cash wallet that you control directly, like a desktop or hardware wallet, then you can usually recover your lost Bitcoins by importing the private key of the BitCoin Cash Wallet into a BitCoin wallet.

BTW, the exchange can recover it, too, and they probably will eventually, but they will keep it for themselves ...