question about partial index

In PostgreSQL 9.3.3 Documentation 11.8. Partial Indexes Example 11-2
(http://www.postgresql.org/docs/9.3/interactive/indexes-partial.html)
the partial index is created

CREATE INDEX orders_unbilled_index ON orders (order_nr) WHERE billed
is not true;

And the suggested use mode is

SELECT * FROM orders WHERE billed is not true AND order_nr < 10000;

My question is after an update to the billed column is done, will PG
automatically add or remove records whose billed are just set to false
or true to/from the b-tree?

Thanks in advance.