I've heard a couple of different Paizo folks talk about this and they're not really planning to do anything different. Pathfinder is still early in its lifecycle and they don't plan to drop it or launch Pathfinder 2 anytime soon.
A large part of the reason that Pathfinder (the game) and Golarion (the world) exist is so that Paizo isn't tied to the whims and fortunes of another company. The 5e switch is a perfect example of that situation, so I wouldn't expect them to do anything surprising.
I'm sure they have plans to deal with a short term drop or spike in demand, but that's more on the business side then the consumer side. They'll need to be flexible for a few months before and after the 5e release, but I trust Lisa Stevens has that well in hand.
As far as my personal predictions, I'd expect Paizo to see a small short-term drop in orders. A lot of people will at least try 5e and that will strain some budgets. I don't foresee WotC converting that many Pathfinder players, although some have always followed both systems and that number might increase.
Over the long-term, if 5e does well, I'd expect Pathfinder to grow slightly. If 5e succeeds, I expect it to do so by gathering new players. That doesn't hurt Pathfinder at all and some of them will inevitably try out Pathfinder as well.
If 5e does poorly in the long term, it's probably a wash for Paizo but bad for the hobby as a whole. Until Pathfinder becomes the household name rather than D&D, we'd get fewer new roleplayers.
Cheers!
Kinak