I think it will work, but it won't be anything near low dropout. An average N-channel MOSFET has the Vgs threshold at about 1.5-2V. Your opamp output (the gate of the FET) will go close to the positive power rail, so that means the source will be 1.5-2V lower than that. That means at least 1.5-2V dropout.
Also, you will need some capacitors on the input, output and in the feedback loop, so your circuit won't oscillate.
