That a train is so full that nobody can board, is really something that does not happen a lot. When it does, it would probably get the evening news…
And if a train is so full that nobody can board anymore the kind of ticket you have will not matter. All holders of tickets and passes valid for a train have exactly the same rights.
(If you thought that a ticket came with a guaranteed place on a train, then you are mistaken. That is not how trains work.)
But SBB runs engought trains, and runs rather long trains, so it is rare that not everybody has a seat. And even if there isn’t a seat for everybody you can still board, as it is permitted to travel standing as well.
If you want a guaranteed seat on a particular train you need a reservation. Reservations are separate. Few people bother with reservations here though, but if you want one you can get that on www.sbb.ch. However only for the Zurich - Visp part. On Visp - Zermatt you cannot reserve seats.