Order by optimisations?

Hi,

Does PostgreSQL do the following optimisation:

SELECT * FROM diary WHERE date = '2005-05-01' ORDER BY date;

or in fact even better (for my situation)

SELECT * FROM diary WHERE date BETWEEN '2005-05-01' AND '2005-05-01' 
ORDER BY date;

Does it know that the input to the sort routine is already sorted and 
hence is a no-op?

Chris