I think what you want is covered in the Frequently Asked Questions about Advance fares section of the National Rail Enquiries (internal) Knowledgebase (iKB), which isn't available online officially. However, one of the nice members of Rail UK Forums posted that to their site a few weeks back in response to a different query
Q25 - Can a passenger with an Advance ticket travel on an earlier connecting train?
A: Yes if it is non-reservable, no if it is reservable.
An exception that benefits passengers: Where Virgin Trains East Coast is a connecting TOC from Stevenage via London and vice versa, e.g. “AP London-Reading”, or “VWC & Connections”, Virgin Trains East Coast waives the need to travel on the exact Virgin Trains East Coast train booked on this relatively short journey Stevenage ↔ Kings Cross, even though retail systems will force a reservation to be made.
So, it all depends on if seat reservations would've been possible on the connecting train you want to take. If there are seat reservations possible, then an advanced ticket is only valid where you have a reservation on that service. Where no seat reservations are possible, a & Connections ticket is
Checking easily which trains can and can't have seats reserved is probably a different question... If you ask staff at the station about a specific train they can tell you though!