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Yes, your trip to Pilatus is free with the Swiss Travel Pass, regardless of how you choose to get there and back. You will need to present your pass at the ticket window though, to get a free electronic ticket to release the barrier gate you have to pass through before boarding the cogwheel train or cable car.
You can download map showing what is covered by the Swiss Travel Pass.
As explained in the legend on the map, red lines are trains, yellow lines are buses, black lines are cable cars, white lines are boats. Solid lines are free, dotted lines are discounted. Discounts are mostly 50%, but only 25% for transport where you see the number “1” inside circle near the dotted line. There are a few grey lines on the map as well. These indicate transport that is not covered by the pass.
Swiss Travel Pass coverage
http://www.myswissalps.com/sw isstravelpass/validity
Alpenrose