I created a table with a column specified as not null (and an index for that column).  Doing a query on that column where a where clause that as "is null" seems like it would be able to do an order(1) check since no rows can match. 

Instead it seems to do a scan.

Creating the same test but omitting the "is null" column attribute leaves it to use the index.

Perhaps my setup is wrong here but this seems confusing.
sqlite> .dump
PRAGMA foreign_keys=OFF;
BEGIN TRANSACTION;
CREATE TABLE t (foo not null);
INSERT INTO t VALUES(1);
INSERT INTO t VALUES(2);
INSERT INTO t VALUES(3);
INSERT INTO t VALUES(4);
INSERT INTO t VALUES(5);
CREATE TABLE r (foo);
INSERT INTO r VALUES(1);
INSERT INTO r VALUES(2);
INSERT INTO r VALUES(3);
INSERT INTO r VALUES(4);
INSERT INTO r VALUES(5);
CREATE INDEX idx on t(foo);
CREATE INDEX idxr on r(foo);
COMMIT;
sqlite> 
sqlite> explain query plan select * from r where foo is null;
QUERY PLAN
`--SEARCH TABLE r USING COVERING INDEX idxr (foo=?)
sqlite> explain query plan select * from t where foo is null;
QUERY PLAN
`--SCAN TABLE t
sqlite>