I just bought a Breville "smart" dehumidifier and can confirm that if you cut the power, it restarts on the same mode when power is restored.  There is a warning not to switch remotely in case something is left on top of it, but if you can trust yourself not to do this, all should be OK.  Mine is in my boat, and it's quite good being able to control, check it's running and what the humidity is, remotely