Not really. It used to be true in the 1970s; but today appliances consume roughly about the same as space heating, despite decades of energy efficiency improvements --and the culprit is, you guessed it, the rise of consumer electronics [1,2].
And it's not just standby-mode "phantom consumption", as the EPA used to think. Today there are more devices with larger, sharper screens and hungrier batteries to charge, all left on for longer than ever before [2]. And it all adds up.