If you do have a 1st class pass (needed) and don't care about the mandatory reservation fee of 49 CHF per person it's a great experience especially if you do order a snack and drink (recommended) but also a very expensive one. But be aware that Prestige class is just available between Interlaken Ost and Montreux. 

On the other hand it's certainly not necessary. You may have a look at the Belle Epoque train which is also a great experience without the cost of Prestige class. But you'd need to change trains once more.

(You need to change trains in Interlaken anyway, it's no direct train from Luzern to Montreux, that's just marketing.)

You may also consider this: It's possible to leave the first train from Luzern in Brienz and go by boat to Interlaken (recommended). The boat departs directly at the station and does arrive directly at the station, is included and does have 1st class if you do hold a 1st class pass. 

It is also possible to build in a second boat trip from Interlaken if you do like.

And of course it's a much better experience to go by an old steam ship to Genf. You need to change boats for this. But it's not included, you do just get a reduction (50%) and if you'd like to do this directly when arriving in Montreux by Golden Pass there's just one possible connection in summer (16.32 from Montreux) that does start end of June (you did not tell about your travel date). But it's highly recommended. It's especially nice when going by last boat in the evening in summer and having dinner aboard (very good and recommended). 

But especially the timetable for boats do depend on your concrete travel date / time of year. It's also possible (even before end of June) to do not the full boat trip from Montreux (full trip lasts about six hours just in case you aren't aware of this).