As the pilot in command, you'd fly the aircraft as the first priority, then navigate and communicate comes last.
Which means you can do that in all cases of emergencies. You can even swing around and land the aircraft without calling ATC......
Sure, someone will probably ask you why you didn't communicate afterwards, but if you deem that you were too busy...... noone would bat an eye.
At STN, getting airborne and then doing a 180 to land would cause a lot of eyes to be batted!