Does music specifically written as a theme song have a distinctive sound?

I was just having a debate with myself over this issue:

If I didn’t know that the Welcome Back Kotter theme song, performed by John Sebastian of The Lovin’ Spoonful, was a TV show theme, would I still think it sounded like a TV show theme?

I could not, and still can not, come to a conclusion about it. I think that there is something “theme song” sounding about the song, yet part of me realizes that I only feel this way because I have the knowledge that it was, in fact, written to be a theme song.

Am I making sense here?

What do you think?

“Welcome Back” sounds to me a lot like the same style of “good time music” Sebastian did with the Spoonful. If “Welcome Back Kotter” had never existed, the song–with exactly the same arrangement–could still have stood comfortably alongside “Daydream,” “Nashville Cats,” “Rain on the Roof,” and “Do You Believe in Magic.”