GDAL SQL syntax to add field an put values

Because UPDATE is not supported in OGR SQL, as you stated in a comment, you should update the table using the SQLite SQL dialect available in GDAL >= 1.10 with SQLite and SpatiaLite support:

ogrinfo $myfile -sql "ALTER TABLE $name ADD COLUMN code_num integer(3)"
ogrinfo $myfile -dialect SQLite -sql "UPDATE $name SET code_num = CAST(code_06 AS integer(3))"

You can try using the CAST operator as dmci has mentioned like so

ogrinfo $myfile -sql "UPDATE TABLE $name SET code_num = CAST(code_06 as int(3))"

The SQL dialect supported by OGR does not have CONVERT if recall correctly. You can check the docs for more info. Good luck!