If the Folk Club/session is advertised as a for 'English music/song' then possibly a full evening of C&W would be out of place but at an 'everyone welcome' session/singaround a well sung C&W song added in should be fine :)

The session I go to most is more of a singaround with a great mix of songs from traditional to comic, and they put up with me (as a definite non-singer) playing tunes ranging from English to Finnish :)

   They're a tolerant lot