Does El Niño increase the amount of heat that escapes into space, or does it increase the amount of heat trapped on Earth?
During El Niño heat is transferred from ocean to atmosphere. If atmosphere gets warmer, yes, it generates more radiation and more heat escapes into space. The same about land surface - if it's warmer, it radiates more heat. 

Of course that's all with assumption that there are no other factors influencing it - like e.g. greenhouse gases.