It might work, at least "sort of". However, it is hardly too optimum way of building an amplified crystal receiver.
I say "sort of", because there are some questionable aspects in the circuitry. Without some modifications, not even "sort of"....
Regarding the power supply connections: I am afraid this is not a good configuration at all, as the OPAMP output can never swing below the negative rail. Therefore you can't connect the minus pole of 9V to ground, if you want output to be able to reproduce the negative half-part of the AC waveform. The easy fix would be to use two batteries, one +8V and other -9V towards the ground, to feed the amplifier.
Another is lack of RF filtering after the diode. I would at least connect a small capacitance from cathode of diode to ground.
The second is the configuration of amplifier. It is essentially a transimpedance amplifier (converting current to voltage). That might work well. However, it is a bit unusual configuration in this context, and therefore I would analyze and simulate it before "buying" it.
Btw. for analog simulations, a program called LTSPICE is free and pretty intuitive to use for this kind of circuitry. You can download it from Linear Technology (
https://www.linear.com/designtools/software/#LTspice)