Hi Isrida96 -
Nice to see you on the forum:
The general answer to your question is "Yes."
But, there are some details, depending on when you will travel. So, the answer actually depends on when you plan to travel. In parts of November, there is track repair work that requires a bus substitute along part of the route. And, at some times of the year, the Lucerne-Interlaken Express is a substitute running on the same tracks.
However, you can always take the journey over those routes, even though you may travel in regular trains.
This may help:
When will you travel?
You can check your specific dates on the timetable:
The computer that runs the timetable defaults to the fastest routes. The Golden Pass Route is more scenic, but not as fast, as, for one example, going through Bern.
So, for the leg between Luzern and Interlaken, include "Giswil" as a "via" connection to force the choice of route.
For the leg Interlaken to Montreux, include "Zweisimmen" in the "via" connection, for the same reason.
When you have selected a connection, click on "Show all Details" and look at the text at the right. There you will find words such as "Golden Pass" for those particular trains. You can also get a route map.
Try it first on the Interlaken to Montreux route to see how it works.