Do you want to measure what happens in the few milliseconds / seconds when the appliance is powered on, or do you want to continuously log changes in voltage periodically over a long duration of time - say a few hours? If it's the latter, you might be better off getting a high-count multimeter with data logging / SCPI, instead of the oscilloscope.
Suppose you are using those linked probes with your oscilloscope. Assuming you want to do this in Finland, AC RMS is 220V so peak amplitude is about 310V. This means you will have to use the probes with x100 attenuation, not x10. So, the oscilloscope will see a signal going from +3.1V to -3.1V. I think your oscilloscope has an 8-bit ADC. I do not trust oscilloscopes / measurements when a part of the signal is outside the screen. So, in the best case, putting all those 8 bits to bin signals between +3.1 and -3.1V, you get an on-oscilloscope resolution of 0.0242 volts which translates to 2.42 volts of resolution for the line voltage (x100 attenuation).
This means that with the linked probes, you won't be able to meaningfully measure any changes to line voltage which are smaller than 2.42V. I don't know if that's good enough for your application.