No, I can't speed-up evaluation of generic "count(*) where ()" queries this way.
no you can't speed up generic where(), *but* you can check what are the most common "where"'s (like usually i do where on one column like:
select count(*) from table where some_particular_column = 'some value';
where you can simply make the trigger aware of the fact that it should count based on value in some_particular_column.
works good enough for me not to look for alternatives.