The reason for the question is as follows: consider a proton covered with electron cloud. The proton naturally sits around the minimum of its potential energy surface (PES). Consider next an external electrical field (EEF). Classically, when an EEF extracts a proton from its seat inside a negative charge distribution (NCD), it should first bring the proton on the verge of this NCD, in other words the proton will not jump inside-out of the electronic cloud, but rather move gradually to the boundary and therefrom get detached by the EEF. This is classically. If we now bring an external electronic cloud (EC) close to a shielded proton, we could expect that 1) either this external EC penetrates inside the proton's own EC and gets the proton over, or 2) the electric field generated by the external EC is strong enough to fully deshield the proton, as in classical picture, or 3) the proton leaps through its cloud by virtue of tunneling. The 1st route should be ruled out by QM [as I understand, not mixing electronic clouds cannot get overlapped in space], the second requires very strong electron accepting capacity of the proton counter particle (conjugate base), which cannot be taken for granted, so the 3d option seems the only probable.
This is all some background. The question is still there - if tunneling is fully ruled out, will we observe any acidity at all (well, yes, in the kinetic sence, i.e. happening within our lifetime )?