Yup - according to the article here, Roddenberry in fact wrote the lyrics to the song that Alexander Courage wrote (useless fact - Courage wrote the song in a week...). Lyrics are below. Um, yeah, ok, sure.
The rim of the star-light
Is wand'ring in star-flight
He'll find in star-clustered reaches
Strange love a star woman teaches.
His journey ends never
His star trek
Will go on forever.
But tell him
While he wanders his starry sea
Remember, remember me.