In some cases it may work, but it may not sound right for at least 2 reasons:
1. When a chord is strummed, the most prominent note is the highest note in the chord. In the case of C, that's the high C on the first string rather than the lower C on the open third string. It would probably sound an octave high.
2. The chord that goes with that part of the song may not be C. Other chords, such as F, include the note C.
What you're suggesting doing is something like "chord melody." When playing chord melody, often only part of a chord will be strummed so that the highest note played is the melody note.