Do digital balances always represent real money held by banks?

The answer is NO.

The currency in circulation today, known as Money Supply (to make it simpler, albeit there are many different types of the money supply) is electronic in nature.

If you’re asking that US$ 10 Billion (for example) in electronic form has some sort of $10 Billion in notes stored in a safe in a bank somewhere, then that is not the case at all.

It is just the opposite. If there is, for example, $1,000,000 in currency notes in circulation, then the money supply will list it as such, that the notes & coins in circulation are $1 Million.

There is no requirement for the digital money or the physical currency (notes and coin) to be backed up by anything, other than the full faith and credit of the United States government. Hence it is called fiat money.