It certainly can be done and is part of the fun and challenge of the TAMMY project. Conversely, a 4-beat rhythm can be converted to a 3-beat rhythm, or to a compound rhythm such as 6/8. There are also other rhythmic possibilities for a piece originally played in a 3/4 time.
You can practice rhythmic conversion or transformation with perennial tunes like "Moon River", "Silent Night" and "Morning Has Broken". If you prefer some Australian tunes, then try "Waltzing Matilda" and "I Still Call Australia Home".
Just as we do not have to stick to the same key and instrumentation for a piece of music, we can also take liberty with its timing, phrasing, syncopation, and even its time signature.