Fractional reserve itself is not impossible (a bank offering BTC denominated accounts could lend out some of the BTC and not retain enough on hand to cover all deposits.)

But because of the supply characteristics of bitcoin, you'd probably have to charge depositors to store money rather than giving them low-to-zero interest, and give loans at zero-to-low interest compared to typical major fiat currency rates for otherwise similar loans, and then why would depositors pay to store with you rather than keep coins in their own wallet?

So, fractional reserve is possible, but it may be tricky to make a viable business model out of it.