Yes, and the diffraction kicks in at f/8 no matter about equivalence, and the sensors are not shrinking or expanding in exactly the same proportions - if it keeps your life happy and simpler, fine. I prefer to go Rover's "da wide" and "da long" way of lens determination.
Diffraction kicks in at any aperture. Whether you see the diffraction depends on:
- initial sharpness of the lens. There are lenses that are diffraction limited even wide open.
- The size of the imaging sensor.
- The resolution of the imaging sensor.
- The print size.
Lets say you have a 20mp MFT sensor, and a 20mp FF sensor. Lets say you will make prints the same size, or look at 100% pixel size on a screen. Lets assume lenses of equal quality.
Lets assume you would see diffraction softening kick in at f8 for the 20mp FF sensor. You then WILL see diffraction softening kick in at f4 for the 20mp MFT sensor.
Same for 40mp MFT + 40mp FF sensors. Same for 10mp MFT and 10mp FF sensors. Diffraction softening will kick in at equivalent f-values. Diffraction softening will NOT kick in at the same f-value with a 10mp FF sensor and a 40mp FF sensor. The 10mp lower resolution masks the diffraction softening, where the 40mp higher resolution will show it sooner.
Yet, a 10mp MFT sensor and a 40mp FF sensor will show diffraction softening kicking in at the same f-value.
So, to correct your sentence:
"Yes, and diffraction kicks in at equivalent f-values, provided the sensor resolution is similar"
There is one note to make about diffraction and f-value. The amount of diffraction: size of the hole, and distance the light has to travel after it passes the hole. With different lens designs, the aperture is not always placed at exactly the same position (relative to the resulting focal length). If one says "diffraction softening kicks in at f8 with this sensor", it is a generalization.