It could be yes, there are several electrical bits:
Autochoke heater
Inlet manifold Preheater
Another heater on the front
Idle overrun valve
Temp time valve
The Autochoke and inlet heaters are controlled by the temperature of the engine coolant, in the plastic flange at the front of the block there is a red and grey sender, red is for the autochoke and grey is for the inlet heater.
The heater on the front should get a constant 12v feed, and is earthed through the carb using an earth lead conected between the top of the carb and the rocker cover. The last two control the 3/4 point unit which is responsible for holding the revs up for a couple of seconds when you start the car from cold, which doesn't sound like they are to do with your problem. You should hear a click from the engine bay when you turn the ignition key though.
But I would say you are likely to have a problem with the inlet manifold coolant channel, a common fault is the o'ring seal degrades and blocks the channel so coolant never reaches the autochoke & waxstat, the carb coolant pipes should get boiling hot when the engine is up to temp!