The last years have been mixed for organized labor, such as losing the vote at the Amazon warehouses in Alabama. However, this is one scenario where the deck seems stacked against Paizo. Unless UPW is lying, they already have a majority of eligible employees, so Paizo will be fighting an uphill battle to win an election, and firing the employees in question would probably wreck them as they lose most of their talent (leaving aside what the NLRB will do to them).
I haven't been buying any Paizo products in a while, not out of principle, but I simply haven't been playing Pathfinder or Starfinder. However, should Paizo recognize the union, I will absolutely start buying Paizo products again.