I Can Cooper Pairs in Superconductors Interact Over Long Distances?

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Do the de Broglie wavelengths of Cooper pairs, in a superconductor, overlap one another, over distances of say hundreds, or thousands of lattice spacings?
 
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Unfortunately I typed the above question just before leaving a coffee shop, and didn't mean to say it that way. I've long known that Cooper pairs of opposite spin form boson states due to phonon interaction over 100 to 1000 lattice spacings, and that because there are many intervening mobile electrons that Cooper pairs change partners constantly over a distance of up to 1000 lattice site spacings, as their wavefunctions overlap.

The question I had in mind was.is it possible for the wavefunctions of Cooper pairs much more distant apart than 1000 lattice sites, say 100,000 lattice sites (or more) to interact with one another?
 

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