Yes. If your first sector is an international flight, your bags will be checked-in all the way to the final destination on your airline booking.
You must conform with local regulations in the normal way. For instance when connecting through an airport in the United States, you will usually be required to collect your bags at the reclaim area, clear Customs, and place your bags on the transfer belt. If this self-transfer is required, you should be informed by your airline when you land.
Please note that itineraries departing from Manchester Airport and connecting via London are not currently available with the bag check-in service.