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It depends on what you consider processing. The Op Amp will consider the digital signal as analog one. If the Op Amp receives a 0...5V signal for example, it can amplify it, attenuate it, add another signal to it, subtract another signal, filter it, etc, whatever an Op Amp can do to a signal.
If, by processing, you mean Digital Signal Processing, as in data processing, no, it cannot do it.
OPA4658 output is bipolar, while the input of 74HCT04 is unipolar. So, make sure you limit the op amp output voltage to the positive region.
Even so, you cannot just power the opamp between 0 and 5V, because the opa4658 output low level is about 2.3V from rail so the HCT04 will not be able to "see" a VOL level in its input. You will need to drop the op amp negative power supply input below ground by 2V to be able to drive the input of HCT04.
Another solution is to use a different op amp like a rail to rail one, that can drive its output close to the rails. Make sure it has a good slew rate as previously stated.