Yes. All the lights on the dash (engine management, ABS, airbag etc (if these are fitted to your car)) should come on with the ignition then go off when the engine starts.
The only one which should stay on is the handbrake/brake fluid level light, which should go off when you release the handbrake.
Your car will fail an MOT if the EM light is not working.
hth, November 2009