You're assuming correctly. While Swiss doesn't 100% say so, their text is pretty much clear: You will receive the barcode for your journey with SWISS Air Rail when you check in. If it is not possible to check in, the barcode is also printed on your eTicket for the train journey within Switzerland. You can have this sent to you by email.

I'd suggest to checkin online for train segments, still (To make sure miles are credited correctly, plus, this might get you a free ride to the airport as a bonus if you're coming partially from that direction, as you can take ANY* train towards the airport, doesn't have to be the direct intercity trains.. )

* I love it how Swiss TRIES to tell it's customers that they should take the train booked, but actually ANY train is fine if there had been travel changes... so yes, for example, if you're living in Spreitenbach and having booked AirRail from Geneva, you can take the S-Bahn to Zürich HB, then connect to another train to the airport, with your Swiss ticket (or boarding pass)

You must in principle use the SWISS Air Rail connection you booked. This applies in particular on international SWISS Air Rail routes to places close to the border outside Switzerland. There is a rail connection on these routes, which means your SWISS Air Rail Ticket is only valid on the specific train you booked.

If there are any travel changes, your existing ticket also remains valid within Switzerland for the route and destination concerned for one day before and one day after your planned journey.

https://www.swiss.com/ch/en/book-and.../swiss-airrail