Table with clustered index implicitly sorting by unique nonclustered index
No, sorting is not implicit and should not be relied upon. In fact, in the first tooltip, you can see that it is explicitly stated that Ordered = False. This means SQL Server didn't do anything at all to implement any sorting. What you observe is just what it happened to do, not what it tried to do.

If you want to be able to predict a reliable sort order, type out the ORDER BY. Period. What you might observe when you don't add ORDER BY might be interesting, but it cannot be relied upon to behave consistently. In fact in this post, see #3, I show how a query's output can change simply by someone else adding an index.


T-SQL Tuesday #56 : Assumptions



  What is SQL Server's preference in choosing the UQ?


The UNIQUE NONCLUSTERED index contains the clustering key, so it is covering for the query. In this case, your table only has two columns, so the clustered and nonclustered indexes contain the same data (just sorted differently). They're both the same size, so the optimizer could choose either. That it chooses the nonclustered index is an implementation detail.

I call this a "coin flip."