According to general relativity acceleration is identical to gravity, hence a nonlinear phenomenon. The linear superposition principle cannot hold. So there should as a whole be a connection to wave function collapse. One further point. We don't need coherence of any kind for the quantum speedup principle.
Coherence can refer to many things.
The quantum speedup principle does not exclude the possible importance of coherence for the organism. And it may be possible for coherent effects to occur at body temperatures. I can perhaps here draw attention to a model I developed some years ago, which might be called the proton supermobility model. We reverse the picture at the water-membrane interface. Mobile protons migrating in the layer of bound water adjacent to the membrane and enveloping the macromolecular components of the cell polarize electrons in the polar head groups of membrane lipids, thereby leading different proteins to be attracted to the same charge distortion and therefore to each other.