Yes. Actual crypto is stored on several (mostly cold) wallets, and what you see in your exchange account is just a number. When you withdraw crypto, it gets sent from one of the exchange’s wallets.

But as long as it’s on the exchange, your account is just a number on a paper, so to speak. This is important for the exchange’s function though, as it allows you to trade crypto without paying chain commissions.

Any trading/swap operation is just a switch in paper numbers.