411A quote (6th june 06):
Well actually, KLM'er, he was busy at the time, raising the landing gear, silencing the fire bell, pulling the respective engine fire handle and discharging the engine fire extinguisher.... among other things.
This sounds like your f/o was the Pnf and you as the Pf.
So, you are very busy flying the aircraft (with a reduced capacity as it is a non-normal situation), he is very busy with the list you gave above, and you STILL feel that it is not a good idea for a simple:
"MAYDAY, MAYDAY, MAYDAY, "callsign", Engine fire ... standby"
considering that during your poor Pnf's drills, ATC may have tried to communicate with you (not realising your situation), distracting your Pnf, who may then possibly lose his place or miss a critical part of his drills ... or if you are capable of recognising his high workload, you answer, using up yet more of your capacity possibly distracting you from your flying duties ... need I really continue ?
I know the rules as well as any ... aviate, navigate, communicate.
BUT, if saying a quick sentence (which can easily be cancelled once the high workload is complete) is going to improve capacity (should an additional situation arise), performance and provide a helpful service from ATC, it is not only unprofessional but utterly STUPID. Even if you decide not to answer, that dealing with your situation is more important, the fact they are there, trying to get in touch, is going to be a completely unnecessary distraction.
Within the european area, anything other than a MAYDAY might confuse the controllers who in my experience have a limited grasp of the english language anyway and push your workload (without your knowing), through the roof.
Not all pilots have the comfort you may enjoy in the USA where everyone is fluent in english !