If you can't doublespend, you have no chance of creating any fractional reserve. You can lend your "fake bitcoins", but that is useless to everyone else not part of your system.
I'd say we're not that far from such a situation. Many people already fall for "wrapped" Bitcoin, which it nothing more than a promise to real Bitcoin coming from a company hiding in the Cayman Islands. And yet, people fall for it.
I wouldn't say they "buy" bitcoin. When you can't put your bitcoin to a bid or ask, nor can you spend it on-chain to some merchant, then you don't have it, nor can you affect the price howsoever. You're completely outside the system. A "promise" of bitcoin is more like a bet that you would put in a broker.
Let's say that I open up a bitcoin bank, with zero bitcoin, only dollars in reserve, and I sell bitcoin promises. If these promises can only be redeemed for the bitcoin price at the time the redeemer decides in exchange for dollars, then he's just placing a bet that bitcoin will go up; does not affect bitcoin economy in any way.
Now let's say that I open up a fractional bitcoin bank, with zero dollars and zero bitcoin in reserve. For every dollar I get in exchange for bitcoin promise, I only buy 10 cents worth of bitcoin without anyone knowing (practicing fractional reserve, with 10% in reserve in secret). If I grant my clients the right to withdraw bitcoin promises for real bitcoin, then it's a betting platform for 90% of the coins, and a custodian for 10% of the coins. (Of course I risk going bitcoin-bankrupt, but let's ignore it for the sake of simplicity.)
So, essentially, one could claim that clients in those banks are "tricked" into believing they're buying bitcoin, while they're placing a bet on bitcoin, but I'd counter-claim that since they did not withdraw immediately, they weren't looking to buy bitcoin in the first place. What they would want, is to bet that it will go up.