You can't take off in freezing drizzle, only light freezing drizzle. You can taxi single engine in icing conditions. Main problem with engine icing is when it is running and sucking stuff in coupled with a pressure drop at the inlet.
After you get deiced you will start both up (if they weren't running) and take off shortly afterwards.
The CFM 56 only the fan cowl is heated by bleed air. The spinner is heated by engine oil and the fan blades are supposed to shed the ice (that is what the engine run is for). Most of the time the engine run 15 seconds is done in postition on the runway before takeoff so no jetblast problems and as long as it all looks good you just advance the power and go.