No, the amount they can lend out is mostly based on their capital. If they want to lend money out but they have reached their capital adequacy limit, they have to capital raise by issuing new shares for cash, not seek more deposits. (I’ve been a bank shareholder when they had to do this, when the Basel III rules changed the limits to make things more stable).

Deposits are liquidity that help grease the wheels, so it’s necessary, but it’s actually more the transfers of money moving in and out that they need, not liabilities sitting on their balance sheets.