In district I, A wins (in most Condorcet methods, anyhow).
In district II, (same as district I but the roles of B and D are swapped),
A also wins.
But in the combined 2-district country,
C is the Condorcet winner (beats A by 8:6, beats B and D by 9:5).

Consequently,
some Condorcet methods cannot be "counted in Precincts."
For example, the Smith,IRV method
invented by Woodall
is Condorcet but I see no
efficient way to count it in precincts if there are a large number
of candidates (say 100 candidates, if you want something concrete to
think about – see any feasible way to count it other
than a centralized count? I don't).

However, the Condorcet methods that depend only on the matrix of "pairwise totals"
can be counted in precincts (despite the nonadditivity paradox illustrated above!)
in the sense that each precinct can find and publish its pairwise matrix
and the summed matrix
will be used for the whole country.