Not really, no. Two reasons,
MOSFETs are in a sense voltage controlled devices, they turn on or off (or in between) based on the voltage between the gate and source (it's really the charge on the gate, but I find this analogy works well), BJTs are controlled based on the current flowing from the base to the emitter. These control methods are just too different to drop into q circuit like this one. (Source and emitter become drain and collector for p channel feta and pnp BJTs, respectively).
Next, these transistors are operating in their linear regions, not in saturation. They're 'half on' instead of all on or all off. This means the circuit uses their transfer characteristics, in this case that the emitter current in an npn bjt is linearly proportional to the base current. This isn't the case for fets, since they aren't controlled with a gate current.
The equivalent circuit is entirely possible to make with FETs, and it might look similar, but odds are it won't be exactly the same.
Is there any particular reason you want to simulate the 7805? It might be easier to duplicate a certain property if it differently in simulation than to replicate the entire thing.