I would have thought only if its an old or poorly maintained, or damaged fan or aircon unit. Decent ones should have built in circuitry to stop them putting out spikes back to the mains.
If you are worried you can always plug in some transient protectors...eg, a board containg MOVs.......or say, a HV capacitor board at the output of a FWB....these steps will have clamp any transients.
But you can always make a "transient catcher".....use eg a 450V LR8 linear reg at the output of a FWB....it will blow at the slightest high mains transient.
Maybe just set it up powering a led at 1mA or so......then see , over time, if it blows. Obviously dont put a filter in front of it.