You want to appear to be professional. People usually respond favorably when they see someone smiling. It helps them to warm up to the individual. Smiling seems to help build credibility, at least when they are speaking to a group.
I am lead to believe from a Russian colleague that if a fellow Russian was smiling, the automatic response would be “I wonder what they are hiding?”
While smiling would seem appropriate, what about a picture where the individual is laughing? Perhaps if you were in the entertainment industry, it might be appropriate. Not so much I would expect for a Funeral Director or maybe even a Banker.
In a less literal perspective of smiling, I believe that our promotional content should be written from a smiling perspective. I have read copy and have said to myself “This person must have been angry when they wrote it.”
So I say, have fun with your Linkedin profile and let your smile shine through your headshot photo and your promotional copy.