Not quite. A full backup will backup the database and enough of the log to recover the database when it is restored, but it will not truncate the log. So if you are running a database in FULL or BULK_LOGGED recovery, the transaction log will continue to grow if you are only doing full backups.
See this topic in BOL 2005:
ms-help://MS.SQLCC.v9/MS.SQLSVR.v9.en/udb9/html/4d933d19-8d21-4aa1-8153-d230cb3a3f99.htm
Scott Duncan
MARCUS. Why dost thou laugh? It fits not with this hour.
TITUS. Why, I have not another tear to shed;
--Titus Andronicus, William Shakespeare