Shytorque
You are correct in your statement of zooming to height but you have over egged it slightly.
A Hawk at LL (let’s assume 420 knots) that suffers a catastrophic engine failure can expect to achieve somewhere in the region of 5000’ AGL and establish a 190 KIAS glide. This assumes it is flown in an energy efficient way.
I will reiterate that I know nothing about the accident in question and the bird strike idea is still theoretical.
BV