Apparently not. The Disneyland location that opens on Main Street USA in a few weeks will have indoor seating. They made a point of mentioning that on the Disney Parks Blog and in the Starbucks preview in the Blue Sky Cellar. (Yes, there is a preview center for Starbucks at Disneyland.)
Here's the schematic drawing of the Disneyland Main Street seating area inside the new Starbucks, from the Blue Sky Cellar preview center at Disneyland Resort.
The Disneyland location won't have as much seating as the Starbucks in DCA, but it will have about 32 seats around tables and wall booths according to that schematic drawing. Plus some chairs around the old pot-belly stove they are saving from the old location.
Not sure why they went so big with indoor/outdoor seating at Starbucks in Disneyland/DCA, but appear to have nixed it entirely from the Starbucks in WDW? Baffling how the Disney company works sometimes, especially between Florida and California.
Indoor Seating at FF&P Starbucks on Buena Vista Street at California Adventure
And outdoor seating along the Buena Vista Street sidewalk in front of Starbucks