I had a ticket last week from LHR to Eglington Airport with no ticket number showing in the app. The connecting flight (a different BA flight number)to John Lennon Airport did have a 125 number in the reservation. I checked in and travelled on both legs with no issues.
Post travel i received tier points and avios for the second flight (the one with the ticket number) and nothing for the first flight. BA are still trying to puzzle out how to award me what I'm due because there wasn't a ticket number showing for that leg.
Am not recommending travelling without a ticket number, am just saying.