Is it possible to send BTC out of an exchange account, in order to bypass the private key management system Inspired by this other question, I wanted to ask a question related to how the private keys are managed by the different exchanges.

The question is: do any of the exchanges allow the sending of bitcoins to external wallet addresses?

(My reason for asking this is that I was thinking it would allow the user to send bitcoins to an address controlled by himself and then get around the enforced private-key management system.)
Yes, all exchanges allow this.  They have to, because this is how you withdraw or spend coins from the account.  It's not any kind of sneaky workaround, just normal behavior.  

However, you can only trade using coins (or dollars) that are held on the exchange, so if you do this, you won't be able to sell them on the exchange until you send them back (redeposit).  This incurs another transaction fee and takes time for confirmation, so it's not an option for people who want to be able to trade rapidly or sell their coins quickly when the price moves.

(Decentralized exchanges may be an exception.  I know less about how they work.)