GPS would, in fact, work
totally fine if the effects of general relativity were exactly zero. The software does, however, need to apply adjustments to account for effects of GR, in order to produce precisely accurate results.
A particle accelerator is a tool used for conducting science experiments. That they work, for that purpose, is purely a product of engineering.
At issue is not "whether science works". It is, rather, what percentage of published papers in science journals are crap, and advance the field not at all. The people in the best position to know say they are appalled at how many are.
Would they all say 80%+? Obviously not. Do any? Absolutely.