Two surfaces, in intimate contact, for 'prolonged' periods, become "cold welded", as electrons from each surface, bond to the other. Is this a manifestation of Quantum Tunneling effects ? If two perfect crystalline lattices were brought together, with perfectly smooth faces, would they "meld together", into a single block ??

The proximity removes the barrier that would require tunneling, so no.

 

There is no such thing as a perfectly smooth surface.

Could you say, that the "evanescent tail" of the electron [math]\Psi[/math], extending (slightly) up & off the surface of one of the blocks, would "enter" an available Molecular Orbital in the other block, and thereby form into a new, both-block-spanning Molecular Orbital ?

Maybe but you've got some serious symmetry considerations to account for.