Yes, that is effectively what happens. Left-hand running through the main Arlanda tunnel, with two spurs to the Arlanda Express stations at Arlanda South and Arlanda North swapping to right-running because of the configuration of the underground junction.
OpenStreetMap has the most accurate mapping of the railway lines under Arlanda. If you click on this link…
OpenStreetMap is a map of the world, created by people like you and free to use under an open license.
www.openstreetmap.org
… you should see that the northbound line from Stockholm Central towards Arlanda South and Arlanda North diverges from the main line inside the Arlanda tunnel. It diverges to the left (west) then line then passes over (or possibly under… but I think it’s over) the main line.
Once it has crossed to the east side of the main line, it joins a shorter southbound spur which is in between it and the main tunnel. This means they’ve swapped sides.
If that sounds complicated it also hints at the absurd amount of engineering required for these three stations, all of which serve a relatively small international airport. The stations are within about 150 metres of each other, and the terminals are now partially connected airside and completely connected land side. You can technically ride the the Arlanda Express for free between Arlanda North (T5) and Arlanda South (T2) but the time taken to descend to the station, ride the train and ascend to the terminal is about the same as just walking.