Well, sure. Unless you somehow stumble across an opamp that doesn't have ESD protection. Should be rare to non-existent these days, but still. Looking at the datasheet for good ol' LMx24, this is documented and specified behavior, so fair enough.
Is it? I looked at 3 LM324 datasheets. Only one specified an abs max input current for -ve voltages. That one also helpfully noted
"thereby acting as input diodes clamps. In addition to this diode action, there is also NPN parasitic action on the IC chip. this transistor action can cause the output voltages of the Op-amps to go to the VCC voltage level (or to ground for a large overdrive) for the time duration that an input is driven negative."
So pull current out of an input and all op-amps in the package might output one rail or the other.
I expect you can find more datasheets with abs max current ratings, I would be surprised if you find one that provides any specifications for operation with current being drawn through the clamps.
The op-amp also needs to recover from gross overdrive in less than the rise/fall (to clip limit) of the input signal. The op-amp common mode range still has to include the signal +ve peaks and output range has to include ground (which rules out the LM324). The input impedance is low and asymetric. The clipping is only as symmetrical as the matching of the two resistors on the second amp.
So a generally shitty circuit with lots of provisos uses two op-amps, a comparator and some resistors to replace two comparators and some resistors - way to go.