Yes, as of version 2.12. Outscore now shows your full outreach pipeline per contact: request sent, accepted, first message sent, first reply received, and the latest message with who sent it. You get a sortable Replied column, a per-contact timeline, and a Sent to Accepted to Messaged to Replied funnel on the Funnel page. Privacy stays tight: Outscore stores derived timestamps plus one latest-message preview per contact, on your device; a full conversation is kept only when you save it, and only on your device, and logging a whole thread to your CRM is an explicit per-conversation click that goes browser to your CRM.