So I went to my iTunes music folder and dragged an mp3 file to the startup window. Scheduled a startup, and then shutdown my Mac. Upon startup, my Mac opened iTunes playing the song I specified! It opens in the library and continues to play after finishing the specified song; turn off shuffle if you want to continue playing the same album.
Since it won't play from a playlist, I had to find a workaround. I made a "morning" playlist of songs I wanted to hear and then encoded another version of each song, which I then made another playlist with. Then I changed the artist of all songs to "iTunes Alarm." Now when computer starts, it plays from the beginning of "iTunes Alarm" songs. You must have shuffle off to play the songs in order.
[robg adds: There are some additional hints on using iTunes as an alarm clock, but this seems like the simplest method if you shut down your machine every night.]

