Yes. If you have an ongoing conversation with someone on-site and you unpublish your profile, hiding it from public view, they will still be able to contact you.
Additionally, you will also still be able to contact them.
To contact someone you have an ongoing conversation with, visit your Inbox and select the conversation with them. Once open, type your message in the space provided and click Send.
All messages you send and receive will appear in your Inbox, as will any call you place or receive.