Yes as that’s the shortest route, assuming you’re happy to walk between Warrington Central and Bank Quay.
Almost! The shortest route by rail is 22.66 miles (via Hag Fold & Deansgate).
The route via Warrington Stations, which requires a walk, is 0.3 miles shorter than the shortest route, and is therefore a permitted route.
National Rail doesn’t show the route as valid for some reason, which isn’t very surprising, as it isn’t a very good website.
This is because some time ago, the routeing on the ticket was changed from "Any Permitted" to "Metrolink Ctlz"; the intention being to provide additional validity on the Metrolink for passengers changing between Manchester Stations.
There is no compulsion to use the Metrolink, but ticket booking sites treat this as a "via Manchester Stations" restriction, which is denying the route via Warrington being validated as a permitted route.
Similar problems occur with, for example, Manchester Stns to Watford Jn route: "+via London"; booking engines cannot offer an itinerary on this fare unless you travel via London Terminals, despite the ticket clearly being valid on the direct route via Rugby without any requirement to double-back.