As a general rule, in Switzerland you buy tickets for a route and not for a specific connection. Thus, yes, the Saver Day Pass is valid on any connection on that day.
The only ticket which is tied to a certain connection/train is the Supersaver ticket. This is only valid on the trains as indicated on the ticket.
Reconsider the Swiss Half Fare Card should you spend more than CHF 240 per adult on tickets for all your planned journeys in Switzerland.