I don't find it inappropriate. Therapists are human beings and they have lives outside their jobs. The person was merely in a public space waiting for the therapist to come out. I don't see the harm? It might be different if they were in the T's office and then perhaps there may be confidentiality issues.
I can see however how it might evoke certain feelings in a client who sees this and make them feel somewhat uncomfortable which is not ideal but not inappropriate IMO.