Of course, you are right, on such a "safe" gyrocopter like RAF,
with high thrust line and no horizontal stabilizer,
on engine out you will have a dramatic nose up moment,
which you have to correct immediately.
Centre line thrust machines or equipped with effective horizontal stabilizer
in the prop wash will remain in level flight or have an automatic pitch down reaction
on engine out..
I thought you quoted "modern gyrocopter", not such death traps like RAF.
Fly safe.
And, thank you, I have enough friends who fly with me on regular basis.