It is unstable. In a normal, stable aircraft pushing the throttle forwards won't result in the plane pitching the nose up.
The plane however wouldn't be as unflyable as it is with appropriate training and without the helpful software that flies the plane into the ground.
It'd just have the the dodgiest set of flying charismatics since the Sopwith Camel's infamous control issues on taking off and landing. (And to be fair the Camel probably wouldn't kill as many of it's own pilots these days given that you could now fly it in sim before flying it IRL...)