Not sure what you mean by I(out) and I(in), current is conserved through the regulator -- it's just a series element. But Vin and Vout will differ, when the reg is doing its job. You wouldn't get a sharp yes-or-no indication with an LED+resistor, but that would work, yes (lit, slightly or a lot, versus completely dark).
The main downside is the supply isn't a constant regulated voltage source, but has a Thevenin resistance equal to R1 when it's not in current limit mode.
It's not a big deal in the first place, because SMPS like that have internal current limiting. They can't deliver DC fault current, not like a transformer and rectifier can. But they do have a lot of capacitance on the output, which can destroy transistors in a hurry.
An active current limiter strictly prevents an excursion of current, whereas a current limit upstream of capacitors cannot do anything to limit the current drawn from the capacitors. So that's the primary benefit you stand to gain, using a circuit like this.
HTH,
Tim