Beginner's question about Dave's power supply EEVBlog #221

[helix1]

in Dave's power supply episode, he puts the current sensing circuitry before the voltage regulator. This means that the op amp has to be rail to rail, as the power supply to the op amp is at the same voltage as one of the inputs to the differential amplifier. If I wanted to adapt this to a non-rail to rail op amp, would it be ok to put the current sensing circuitry after the voltage regulator, but still power the op amp from the unregulated supply? If not, why not?

Thanks in advance!