That's how we mass-produce sodium silicate today, for example for foundry cores and waterproofing concrete. You have to get the quartz (from granite or otherwise) pretty hot for this to work. Pottery kiln temperatures.

Normally you purify the quartz first, but here we're discussing what molten washing soda would or wouldn't do to granite. The quartz in granite normally forms a continuous phase, so as long as the quartz remains solid, the granite will remain solid.

Granite melts at a lower temperature than pure quartz, and I'm not entirely sure it wouldn't just melt before the washing soda had an effect.