No, Sam Smith doesn't play a musical instrument - he admitted as much in an interview with Hunger TV:
I have to be honest, this kind of confuses me. In terms of creative input, it seems a little strange to me that Sam has a writer AND a musician who help him write tracks.
"I don’t play a musical instrument, I kind of chose not to because I feel like sometimes when you play you can over complicate stuff. I like to go into the studio with the musician and the writer and just work with them."
(full article here: http://www.hungertv.com/feature/interview-sam-smith/)
It's the same deal with most "artists" these days though... And I guess as long as the music is good, why should we complain, right?