No, but I'm fairly sure Charles Napier (who played Adam) did write them himself. Not surprisingly, when Napier later appeared on DS9, he asked to play the most un-Adam-like character possible.
On the La-La Land set they are called "Lookin' for a New Land," "Like Hail," "Hey Out There!" (with Deborah Downey also on vocal) and "Headin' Out to Eden." Napier does have co-writing credit. I'm sure @Indysolo could give more information on the track titles.
Cool. Right now the songs don't have any MA articles of their own. Do you have a link to an image of the page you're referring to?
^ Indysolo was one of the producers of Star Trek: The Original Series Soundtrack Collection. And, he will not say it but I will: It is an outstanding work, and any serious OS fan will find it will enhance their appreciation of the show immensely. And it's still available: http://www.lalalandrecords.com/Site/STTOS.html