Do centralized exchanges misrepresent their Bitcoin holdings?

For example, would an exchange of Bitcoin hold accounts for 100,000 customers, and they collective have 8000 bitcoins, but the exchange itself does not hold 8000 bitcoin, but only 1600 for customers to redeem (to transfer to their own wallet if they want to), and therefore, inflating the bitcoin supply by 6400 bitcoins?

It's certainly happened before when there was less regulation or among the smaller, less-regulated exchanges. Whenever an exchange disables withdrawals for everyone, it could be due to them running into liquidity issues like that.

Large exchanges are now regulated by various money services authorities in part to prevent this exact scenario.