No worries. The merger won't affect this at all. As long as an airline has a ticketing agreement with the airline you are connecting to you will have no problem.

Nonrev baggage is usually tagged so at checkin. Once you are cleared for the flight the nonrev tag is pulled from your bag and your bag is sent to the final destination.

Sometimes when you check-in, if you are a nonrev connecting to a different airline, the agent will only check your bag to a connecting city because. This has only happened to me a couple times. Usually at checkin they ask you for your final destination and will check your bags all the way through.