But, the exchange might ask you to verify your account, after you complete it, the exchange either allow you to use their service, confiscate your coins or return back the coins to your address.
Even in a verified account, exchanges will still raise awareness if they ever detect something; they just don't go about attacking accounts with mixed coins deposited in their accounts unless those exchanges frown upon that from the beginning.
If not, they can only trigger an investigation on the user account if they ever have trace of any tinted coin or if the address sent directly to the exchange account is under investigation.
Just like in the case of SB, most of the signature participants who use Binance to receive their payment were asked to fill out some query form about their relationship with that address after the authorities put it under watch.