Yes, but first let me explain. A demo can mean anything from a micro-cassette type recording of someone singing a melody to a fully produced master, complete with strings, brass, background vocals, etc. Should you make a recording of your song? Absolutely. Does it need to be an expensive recording? Absolutely not. Song demos (as opposed to artist demos), should be simple, inexpensive recordings. They are intended to showcase the song not a producer or a percussionist or a vocalist. If you need to just archive your songs, a cassette work tape is sufficient. If you’re planning to pitch your songs, a clean, professional-sounding guitar vocal recording or a piano-vocal recording is very effective.
Excerpt from "The Songwriter/SPublisher Relationship" by Don Cason, found in The AGMA Music Curriculum - Tools for Ministry and Career (1999, GMA, out of print).