Thank you BurgessDonnelly and keithnuttle for your helpful responses which answer my query regarding whether Ancestry retains a record of emails sent, and where these can be found.
I find that I AM able to search for my contact via Ancestry Member Directory Search Basic Information, although the Member Name is not recognised, only the tree owner name.
My email to my contact is not listed on Recent Member Connect Activity, Home Page. Perhaps this is because this page relates only to incoming, not outgoing, messages?
It was suggested that I can request a copy of my email to a member when composing a new message. How is this done?