This is what the warranty says on their main page:
GAME & ACCESSORY WARRANTY
Nintendo warrants to the original purchaser that the product (games and accessories) shall be free from defects in material and workmanship for a period of three (3) months from the date of purchase. If a defect covered by this warranty occurs during this three (3) month warranty period, Nintendo will repair or replace the defective product, free of charge.*
Also, it's important to note that damaged screens are not covered by warranty. Let's hope your console gets shipped to you with the greatest of care.
Well, again, we have laws to protect consumers from these sort of things, so what the company policy is might not matter depending on what part of the world you're in. Here in Norway you've got a mandatory 3 year warranty on all electronic products, and Nintendo has to uphold those. Free of charge.
As for the dead pixels, that is not simply a damaged screen. People are reporting dead pixels with their Switch already. That is a defect, and again depending on what part of the world you're in, Nintendo is required to fix it for you. Free of charge. Regardless of what they say on their own websites regarding 'policies'. So again, I wouldn't worry until we start hearing reports about people being refused support.
That said, it's super shitty of them to even have that stance to begin with, and they're not alone in doing this, though again I doubt it's actually going to keep you from getting proper support - if Nintendo starts doing that then it's time to be worried about the company's futute.