Not sure if time would really permit a mayday call shortly after takeoff with an
engine failure on a twin???
Aviate
Navigate
Communicate.
This baffles me if reports are correct???
And they are probably not...
It's not unreasonable to think that this is the most stressful position you could ever be put under (not just your own life under threat but that of your pax), so it's possible that some actions may have occurred out of order or concurrently.
At this point who is to say that he didn't perform every other action perfectly as well, therefore the radio call had no impact positive or negative on the outcome.