The power supply via the dummy battery isn't going to drop off cleanly when you cut off AC power to it. Once the smart plug shuts it off, the voltage to your camera is going to decay fairly rapidly from normal operating to near zero. The behavior of the camera will be unpredictable and random when the voltage transitions from normal to zero while the camera is still turned on and some of those random results may be bad.
As an example, when I was heavily using my 1D Mark II I needed new battery packs and both Adorama and B&H were back-ordered on the Canon packs so I bought a pair of third party batteries. They appeared to work fine until I tried them at a sports event and the camera would lock up when shooting a sustained burst and require me to remove and re-insert the battery pack to clear the fault. The reason for this glitch was the third party battery couldn't sustain the current needed for these high speed bursts and voltage would drop into that problem region between normal and 0.
Final caution is some power supplies don't behave nicely when being plugged in or unplugged to the AC line and will briefly generate a voltage spike on the output at the instant of being plugged in or unplugged. This is less likely with a well designed OEM supply and very likely with cheaper aftermarket designs which are heavily "cost engineered". Frequent removal/application of power to the power supply while it is connected to an operating camera creates a significant likelihood of camera damage as likelihood of a negative consequence is a function of the number of opportunities for this negative consequence to occur. Forgetting to turn off you camera once in awhile before unplugging the power supply isn't likely to cause damage but do that same thing hundreds or thousands of times and the probability greatly increases.
EOS 1DX M3, 1DX M2, 1DX, 5DS R, M6 Mark II, 1D M2, EOS 650 (film), many lenses, XF400 video
