Does the order of a written redox couple matter?
My understanding is that a redox couple is an unordered pair of two
  conjugate species


This is conceptually perfect and there is no problem when we talk about electrode potentials of half cells because as I had mentioned in your earlier queries, the electrode potential value and its associated sign do not know nor care how you write the half cell.

What is creating confusion in your mind is that you are trying to abbreviate a half cell. Abbreviating a half cell is of no use, because it is creating a problem of ordering.

All we care about the order is when we write a full cell. For that, we must follow the IUPAC recommendation and rules in order to prevent chaos in the published work. There your half-cell is no longer an unordered pair.

I used to remember the IUPAC recommendation with a mnemonic: Write Reduction on the Right.



This has to be parsed as follows: Reduction is on the right, so you must order the copper half cell in such a way that it appears as reduction.  

On the left, of course, we have an oxidation half cell and it must be written as such.

Hope that clarifies your confusion.