The short answer is "YES!!!!!!"
Many folk songs are built on just two chords --- the Tonic (I) and the Dominant (V). In the Key of C major, that would be the C major triad and the G Major triad. Take for example, "Here We Go 'Round the Mulberry Bush." It has just two chords. Many other folk songs and children's songs are built on just two chords.
Even more songs such as folk songs, children's songs, and even hymns are built on just three chords the Tonic or I, the Sub-dominant or IV, and the Dominant or Dominant 7th V or V7. Take the famous song from "Mary Poppins" for example. "Supercalifragilisticexpialidocious" is built on just three chords. The famous hymn "Amazing Grace" is also build from just three chords.


When I was a teenager, my mother bought me a folio of Leslie Bricusse songs. I played and sang all day his songs like "On a Wonderful Day Like Today," "Beautiful Things," "After Today," "Fabulous Places," and "Gonna Build a Mountain" from his many shows like "Stop the World, I Want to Get Off," "Doctor Doolittle," and "Scrooge."

But even two chord songs can be "dressed up" to sound more sophisticated than they really are. Take for example "The Nursery Rhyme Quodlibet" from "The Adventures of Dick Whittington." Four Old English Nursery Rhymes and just two chords. Enjoy!